Question

if an iscoscles right angle triangle has 8cm.find the length of its hypotenuse

Answer 1

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
AC^2 = AB^2 + BC^2
= 4^2 + 4^2
= 16 + 16
AC^2 = 32
AC = √32 cm
[taking positive squareroot because length is always positive]
Hence, the length of its hypotenuse is √32 cm.