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

Question

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

Filo · Accepted Answer

We know that the ratio of the equal side to its base is

3 : 2

For an isosceles triangle the ratio of sides can be written as

3 : 3 : 2

So we get

a : b : c = 3 : 3 : 2

Consider

a = 3 x, b = 3 x

and

c = 2 x

We know that the perimeter = 32cm

It can be written as

3 x + 3 x + 2 x = 32

On further calculation

8 x = 32

By division

x = 4

By substituting the value of x

a = 3 x = 3 (4) = 12 c m

b = 3x = 3(4) = 12cm

c = 2x = 2(4) = 8cm

So we get

S = \frac{a + b + c}{2}

S = \frac{12 + 12 + 8}{2}

By division

S = 16 c m

We know that

Area

s (s - a) (s - b) (s - c)

By substituting the values

Area=

16 (16 - 12) (16 - 12) (16 - 8)

So we get

Area=

16 \times 4 \times 4 \times 8

It can be written as

Area=

16 \times 16 \times 4 \times 2

On further calculation

Area=

16 \times 22

We get

Area=

322 c m^{2}

Therefore, area of the triangle is

322 c m^{2} .

Question Text	The perimeter of an isosceles triangle is 32cm. The ratio of the equal side to its base is 3:2. Find the area of the triangle.
Answer Type	Text solution:1
Upvotes	163

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