Question

The area of an isoscales triangle is 300 cm square. The height of the triangle is 15 cm.Find the perimeter of a triangle. ​

Answer 1

1/2bh is the area of ∆

so, 1/2×15×b = 300.

b = 300/15×2

b= 40

using Pythagoras theorem,

15^2+20^2=h^2

=25.

so, the hypotenuse is the other side.

we know that two sides of an isosceles ∆is equal.

so, the other side is also 25.

so, the perimeter is 25+25+40.

=90cm

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Answer 2

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

Perimeter of an isosceles triangle = 90 cm

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

Given :- Area of an isosceles triangle is 300 cm². Height of the isosceles triangle is 15 cm

To find :- Perimeter of the triangle

Solution :-

Height of an isosceles triangle = 15 cm

First find base of the triangle.

Let the base of an isosceles triangle be x

$\boxed{\sf{Area\:of\:the\:triangle= \dfrac{1}{2} \times Base \times Height}}$

Area of an isoceles triangle = 300 cm²

Equation formed :

$\dfrac{1}{2} \times x \times15 = 300$

$\dfrac{15x}{2} = 300$

$15x=300 \times 2$

$15x = 600$

$x = \dfrac{600}{15}$

$x = 40$

Base of an isosceles triangle = 40 cm

Now refer to the attachment.

Consider Δ ABD

It has one the angle as 90° [Altitude]

Therefore Δ ABD is right angled triangle.

Base = x/2 = 40/2 = 20 cm (Since height of a right angle triangle triangle divides it into two congruent isosceles triangles by RHS congruency and AD = AC)

Height = 15 cm

Hypotenue = ?

Let the hypotenuse be y

In right angled triangle

By Pythagoras thereom

$\boxed{\sf{Height^2 + Base^2 = Hypotenuse^2}}$

Equation formed :

${15}^{2} + {20}^{2} = {y}^{2}$

$225 + 400 = {y}^{2}$

$625 = {y}^{2}$

$\sqrt{625} = y$

$y = 25$

So, Hypotenuse = 25 cm

Now Consider Δ ABC

Two equal sides of an isosceles triangle = 25 cm

Base = 40 cm

Perimeter of a triangle = Sum of all sides

Perimeter of an isosceles triangle = 40 + 25 + 25 = 65 + 25 = 90 cm

So perimeter of an isosceles triangle = 90 cm