The question consists of two statements namely, Assertion (a) and Reason (R). Please select the correct answer. Assertion (A) Reason (R) The sides of the triangle ABC are in the ratio 2 : 3 : 4 and its perimeter is 36 cm. Then ar(Δ ABC) = cm 2 . If 2s = (a + b +c) where a, b, c are the sides of the triangle, then its area is = .

RS Aggarwal & V Aggarwal - Mathematics

Book: RS Aggarwal & V Aggarwal - Mathematics

Chapter: 7. Areas

Subject: Mathematics - Class 9^th

Q. No. 23 of CCE Questions

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23

The question consists of two statements namely, Assertion (a) and Reason (R). Please select the correct answer.

Assertion (A)

Reason (R)

The sides of the triangle ABC are in the ratio 2 : 3 : 4 and its perimeter is 36 cm. Then ar(Δ ABC) = cm².

If 2s = (a + b +c) where a, b, c are the sides of the triangle, then its area is = .

In the given question,

Let us assume the sides of the triangle be 2x, 3x and 4x

We know that,

Perimeter of triangle = Sum of all sides

36 = 2x + 3x + 4x

36 = 9x

x =

x = 4

∴ Sides of the triangle are:

2x = 2 × 4 = 8 cm

3x = 3 × 4 = 12 cm

4x = 4 × 4 = 16 cm

Let, a = 8 cm, b = 12 cm and c = 16 cm

So, s =

=

=

= 18 cm

Now, by using Heron’s formula we have:

Area of triangle =

=

=

=

= 6 × 2

= 12 cm²

Also, if 2s = (a + b + c)

Where a, b and c are the sides of the triangle then:

Area = which is false as it should be:

Area =

∴ Assertion is true whereas reason is false

Hence, option (c) is correct

23

Chapter Exercises

Exercise 7A

CCE Questions

Formative Assessment (Unit Test)

1

In a ΔABC it is given that base = 12cm and height = 5cm. Its area is

2

The length of three sides of a triangle are 20 cm, 16 cm and 12 cm. The area of the triangle is –

3

Each side of an equilateral triangle measures 8 cm. The area of the triangle is

4

The base of an isosceles triangle is 8cm long and each of its equal sides measures 6cm. The area of the triangle is –

5

The base of an isosceles triangle is 6cm and each of its equal sides is 5cm. The height of the triangle is –

6

Each of the two equal sides of an isosceles right triangle is 10cm long. Its area is –

7

Each side of an equilateral triangle is 10 cm long. The height of the triangle is –

8

The height of an equilateral triangle is 6cm. Its area is –

9

The length of the three sides of the triangular field are 40 m, 24 m and 32 m respectively. The area of the triangle is –

10

The sides of the triangle are in the ratio 5: 12:13 and its perimeter is 150 cm. The area of the triangle is –

11

The lengths of the three sides of the triangle are 30 cm, 24 cm and 18 cm respectively. The length of the altitude of the triangle corresponding to the smallest side is-

12

The base of an isosceles triangle is 16 cm and its area is 48cm². The perimeter of the triangle is –

13

The area of an equilateral triangle is cm². Its perimeter is –

14

Each of the equal sides of an isosceles triangle is 13cm and base is 24cm. The area of the triangle is –

15

The base of a right triangle is 48 cm and its hypotenuse is 50 cm long. The area of the triangle is –

16

The area of an equilateral triangle is cm². Its height is-

17

The difference between the semi- perimeter and the sides of a ∆ ABC are 8cm, 7cm and 5cm respectively. The area of the triangle is –

18

For an isosceles right angles triangle having each of equal sides ‘a’ , we have
I. Area =a²

II. Perimeter = (2 +)a

III. Hypotenuse = 2a

Which of the following is true?

19

For an isosceles triangle having base b and each of the equal sides as a, we have:
I. Area =

II. Perimeter = (2a +b)

III. Height =

Which of the following is true?

20

The question consists of two statements namely, Assertion (a) and Reason (R). Please select the correct answer.

Assertion (A)

Reason (R)

Area of an equilateral triangle having each side equal to 4cm is sq cm.

Area of an equilateral triangle having each side a is a² sq units.

21

The question consists of two statements namely, Assertion (a) and Reason (R). Please select the correct answer.

Assertion(A)

Reason (R)

The area of an isosceles triangle having base = 8cm and each of the equal sides = 5cm is 12cm².

The area of an isosceles triangle having each of the equal sides as a and base =b is .

22

The question consists of two statements namely, Assertion (a) and Reason (R). Please select the correct answer.

Assertion(A)

Reason (R)

The area of an equilateral triangle having side 4cm is 3cm²

The area of an equilateral triangle having each side a is (a²) sq units.

23

The question consists of two statements namely, Assertion (a) and Reason (R). Please select the correct answer.

Assertion (A)

Reason (R)

The sides of the triangle ABC are in the ratio 2 : 3 : 4 and its perimeter is 36 cm. Then ar(Δ ABC) = cm².

If 2s = (a + b +c) where a, b, c are the sides of the triangle, then its area is = .

24

The question consists of two statements namely, Assertion (a) and Reason (R). Please select the correct answer.

Assertion (A)

Reason (R)

The area of an isosceles triangle having base = 24 cm and each of the equal sides equal to 13cm is 60cm².

If 2s = (a + b+ c) where a, b, c are the sides of a triangle, then area = .

25

If the base of an isosceles triangle is 6cm and its perimeter is 16cm, then its area is 12cm².

26

If each side of an equilateral triangle is 8cm long, then its area is cm².

27

If the sides of a triangular field measures 52m, 37 m and 20 m, then the cost of leveling at Rs 5 per m² is Rs 1530.

28

Match the following columns.

Column I

Column II

(a) The lengths of three sides of a triangle are 26 cm, 28 cm and 30cm. The height corresponding to base 28cm is……cm

(p) 6

(b) The area of an equilateral triangle is cm². The perimeter of the triangle is…..cm

(q) 4

(c) If the height of an equilateral triangle is cm, then each side of the triangle measures …. Cm

(r) 24

(d) Let the base of an isosceles triangle be 6 cm and each of the equal side be 5cm. Then, its height is ….cm

(s) 12

The correct answer is :

(a)-…….. (b)-……..

(c)-……… (d)-………

29

A park in the shape of a quadrilateral ABCD has AB = 9m, BC = 12m, CD = 5 cm, AD = 8 m and c= 90°. Find the area of the park. [Given: = 5.9]

30

Find the area of a parallelogram ABCD in which AB = 60cm, BC = 40cm and AC = 80 cm. [Given: = 3.87]

31

A piece of land is in the shape of a rhombus ABCD in which each side measures 100m and diagonal AC is 160m long. Find the area of the rhombus.

32

A floral design on a floor is made up of 16 triangular tiles, each having sides 9cm, 28 cm and 35 cm. Find the cost of polishing the tiles at the rate of Rs. 2.50 per cm²
[Take =2.454]

33

A kite in the shape of a square with each diagonal 32 cm and having a tail in the shape of an isosceles triangle of base 8cm and each side 6cm, is made of three different shades as shown in the figure. How much paper of each shade has been used in it?
[Given : = 2.24]