Question

An isosceles right triangle has an area 8sq.cm. The length of its hypotenuse is.......​

Answer 1

An isosceles right triangle has area 8 cm2. The length

(a) Given, area of an isosceles right triangle = 8 cm2

Area of an isosceles triangle = 1/2 (Base x Height)

⇒  8 = 1/2 (Base x Base)

[∴ base = height, as triangle is an isosceles triangle]

⇒ (Base)2 =16 ⇒  Base= 4 cm



In ΔABC, using Pythagoras theorem

AC2 = AB2 + BC2 = 42 + 42 = 16 + 16

⇒ AC2 = 32 ⇒  AC = √32 cm

[taking positive square root because length is always positive]

Hence, the length of its hypotenuse is √32 cm.

Answer 2

Hey..!

Let the two equal sides of the isosceles right angled triangle be x cm.

Area = 1/2 × base × height

8 = 1/2 x^2

8 × 2= x^2

16 = x^2

4 cm = x

Now by the Pythagoras theorum,,

H^2 = x^2 + x^2. (H=hypotenuse)

H^2 = 2x^2

H^2 = 2 × 16. (x=4cm)

H^2 = 32

•°• H = root 32 cm

So,, Option (d) is the correct answer❤❤