Question

the perimeter of an isosceles triangle is 32 cm . the ratio of the equal side to its base is 3 :2. find the area of the triangle?​

Answer 1

Given:

• The perimeter of an isosceles triangle is 32 cm.

• The ratio of the equal side to its base is 3 :2.

To find out:

✯Find the area of the triangle?

Formula used:

• Perimeter of isosceles triangle = a + b + c

• Area of isosceles triangle = b × ¼ × √4a² - b²

Solution:

Let the sides be 3x, 3x and 2x.

✪According to question:-

Perimeter of isosceles triangle = 3x + 3x + 2x

➞ 32 = 3x + 3x + 2x

➞ 32 = 8x

➞ x = 32/8

➞ x = 4

a = 3x = 3 × 4 = 12 cm

b = 2x = 2 × 4 = 8 cm

Now,

Area of isosc. = b × ¼ × √4a² - b²

= 8 × ¼ × √4 × (12)² - (8)²

= 8 × ¼ × √ 4 × 144 - 64

= 2 × √576 - 64

= 2 × √512

= 2 × 22.62

= 45.24

Answer 2

Given:

• The perimeter of an isosceles triangle is 32cm.

• The ratio of the equal side to its base is 3:2.

To find out:

Find the area of the triangle = a + b + c .

Formula used:

• Perimeter of isosceles triangle = a + b + c .

• Area of isosceles triangle = b × 1/4 × √4a² - b²

Solutions:

Let the side be 3x , 3x and 2x.

A.T.Q

Perimeter of isosceles triangle = 3x + 3x + 2x

32 = 3x + 3x + 2x

32 = 8x

x = 4

a = 3x = 3 × 4 = 12cm

b = 2x = 2 × 4 = 8cm

Now,

Area of isosceles triangle = b × 1/4 × √4a² - b²

8 × 1/4 × √4 × (12)² - (8)²

8 × 1/4 × √4 × 144 - 64

2 × √576 - 64

2 × √512

2 × 22.62

45.24

silentlover45.❤️