RS Aggarwal & V Aggarwal - Mathematics

Book: RS Aggarwal & V Aggarwal - Mathematics

Chapter: 7. Areas

Subject: Mathematics - Class 9th

Q. No. 9 of Formative Assessment (Unit Test)

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9

The perimeter of an isosceles triangle is 32cm. The ratio of one of the equal side to its base is 3: 2. Find the area of the triangle.

It is given in the question that,

Perimeter of an isosceles triangle = 32 cm


Let us assume the sides of the triangle be a, b, c and a = b


We know that,


Perimeter = a + b + c


32 = a + b + c


32 = a + a + c


32 = 2a + c (i)


According to the condition given in the question, we have:


a: c = 3: 2


So, a = 3x and c = 2x


Now putting values of a and c in (i), we get


2 × 3x + 2x = 32


6x + 2x = 32


8x = 32


x =


x = 4


Thus, a = 3 × 4 = 12 cm


b = 12 cm


c = 2 × 4 = 8 cm


Now, s =


=


= 16 cm


Area of triangle =


=


=


= 4 × 4 × 2


= 32 cm2


Chapter Exercises

Exercise 7A
CCE Questions
Formative Assessment (Unit Test)

More Exercise Questions

1

Each side of an equilateral triangle is 8 cm. Its altitude is
2

The perimeter of an isosceles right- angled triangle having a as each of the equal sides is
3

For an isosceles triangle having base = 12 cm and each of the equal sides equal to 10 cm, the height is
4

Find the area of an equilateral triangle having each side 6cm.
5

Using Heron’s formula find the area of Δ ABC in which BC = 13 cm, AC = 14 cm and AB = 15cm.
6

The sides of a triangle are in the ratio 13: 14: 15 and its perimeter is 84 cm. Find the area of the triangle.
7

Find the area of ABC in which BC = 8cm, AC = 15cm and AB = 17 cm. Find the length of altitude drawn on AB.
8

An isosceles triangle has perimeter 30cm and each of its equal sides is 12cm. Find the area of the triangle.
9

The perimeter of an isosceles triangle is 32cm. The ratio of one of the equal side to its base is 3: 2. Find the area of the triangle.
10

Given a ABC in which

I. A, B and C are in the ratio 3: 2 :1.


II. AB , AC and BC are in the ratio 3 : 3 : 2 3 and AB = 3 3 cm.


Is ABC a right triangle?


The question give above has two Statements I and II. Answer the questions by using instructions given below:


(a) If the question can be answered by one of the given statements only and not by the other.


(b) If the question can be answered by using either statement alone.


(c) If the question can be answered by using both the statements but cannot be answered by using either statement.


(d) If the question cannot be answered even by using both the statements together.
11

In the given figure ABC and DBC have the same base BC such that AB = 120m, AC = 122m, BC = 22m, BD = 24m and CD = 26m. Find the area of the shaded region. (Take = 10.25)
12

A point O is taken inside an equilateral ΔABC. If OL BC, OM AC and ON AB such that OL = 14 cm, OM = 10 cm and ON = 6 cm, find the area of ABC.

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