Question

Find the perimeter of an isoceles right angled triangle having an area of 5000m^2.(USE√2=1.41)

Answer 1

An isoceles right angled triangle is a triangle in which the two equal sides are the base and altitude of that right angled isoceles triangle .


Given,

Area of the triangle = 5,000 m²

Let , the equal sides are of x length.

So,


⇒ Base = x


⇒ Altitude = x

We know that,

⇒ Area of a triangle = ( 1/2 ) × Base × Altitude

⇒ 5,000 m² = ( 1/2 ) x × x

⇒ 5,000 m² = x²/2

⇒ 5,000 m² × 2 = x²

⇒ 10,000 m² = x²

⇒ x = √( 10,000 m² )

•°• x = 100 m

Now we have,

Base = x = 100 m

Altitude = x = 100 m

By Pythagoras Theroem,

⇒ Hypotenuse² = Base² + Altitude²

⇒Hypotenuse² = ( 100 m )² + ( 100 m )²

⇒Hypotenuse² = 100,000 m² + 100,000 m²

⇒ Hypotenuse² = 2 × 100,000 m²

⇒ Hypotenuse = √( 2 × 100,000 m² )

⇒ Hypotenuse = 100√2 m

⇒ Hypotenuse = 100 ( 1.41 )m

•°• Hypotenuse = 141 m

Now,

Perimeter of any triangle = Sum of all three sides

= 100 m + 100 m + 141 m

= 341 m

The required answer is 341 m.