Question

What are the height (one of the legs) and the hypotenuse of an isosceles right triangle that has an area of 800 square feet?

Answer 1

Answer:

Sides of isosceles are Equal , let them be x

Area of right Angled isosceles Triangle =21×x×x=8⇒x=4 cm

Now, the Length of the Hypotenuse is =42+42=42 cm

Step-by-step explanation:

As the two sides are equal, And square of Hypotenuse i.e Hypotenuse ² = 50,

Let side of the triangle be x,

According to Pythagoras Theorem,

Side² + Side² = Hypotenuse²,

=> As sides are equal, Both are x

=> x² + x² = 50

=> 2x² = 50,

=> x² = 25,

=> x = +5 or -5 ,

But sides can't be negative, 

So the length of the legs is +5

Answer 2

Answer:

Height = 40 feet

Hypotenuse = 40√2 feet

Step-by-step explanation:

Area of triangle = 800 sq ft

800 sq ft = 1/2*x*x = x²/2

x² = 800*2 = 1600 sq ft

x = √1600 sq ft = 40 ft

Hence side = 40 ft

Hypotenuse =√(40²+40²)                 (Pythagoras theorem)

= √(2)(40²)

= 40√2