## Book: RS Aggarwal & V Aggarwal - Mathematics

### Chapter: 7. Areas

#### Subject: Mathematics - Class 9th

##### 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

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