Question

The perimeter of an isoscles triangle is 32 CM the ratio of the equal side to its bass is 3 :2 find the area of triangle
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Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

Given :

Perimeter of an Isosceles triangle is 32 cm.

ratio of two sides to its base is 3:2.

To find :

Area of Triangle

Ratio of the equal side to its base is 3x and 2x

Let the third side be 3x ( Isosceles triangle have two sides equal so I take 3x)

Perimeter is 32cm

Perimeter of an Isosceles triangle =Sum of its all sides

$= > 3x + 2x + 3x = 32$

$= > 8x = 32$

$\bold{x =4}$

Hence ,the two sides of Isosceles triangle is 4cm each.

Third side =2x =32/2=16cm

Area of the Triangle =

$\sqrt{ \dfrac{32}{2} (16 - 12)(16 - 8)(16 - 12)}$

$= > \sqrt{16 \times 4 \times8 \times 4}$

$= > 32 \sqrt{2} {cm}^{2}$

Thus ,Area is $\bold{\red{32 \sqrt{2} {cm}^{2}}}$

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

Given :

Perimeter of an Isosceles triangle is 32 cm.

ratio of two sides to its base is 3:2.

To find :

Area of Triangle

Ratio of the equal side to its base is 3x and 2x

Let the third side be 3x ( Isosceles triangle have two sides equal so I take 3x)

Perimeter is 32cm

Perimeter of an Isosceles triangle =Sum of its all sides

$= > 3x + 2x + 3x = 32$

$= > 8x = 32$

$\bold{x =4}$

Hence ,the two sides of Isosceles triangle is 4cm each.

Third side =2x =32/2=16cm

Area of the Triangle =

$\sqrt{ \dfrac{32}{2} (16 - 12)(16 - 8)(16 - 12)}$

$= > \sqrt{16 \times 4 \times8 \times 4}$

$= > 32 \sqrt{2} {cm}^{2}$

Thus ,Area is $\bold{\red{32 \sqrt{2} {cm}^{2}}}$