Question

18. An isosceles right triangle has area of 8 cm². The length of its hypotenuse is ​

Answer 1

Answer:

√32 cm

Step-by-step explanation:

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

(Name the triangle as ABC)

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.