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Question

Question 1
An isosceles right triangle has area 8cm2. The length of its hypotenuse is

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Solution

Given, area of an isosceles right triangle = 8 cm2
Area of an isosceles triangle =12(Base×Height)
8=12(Base×Base)
[ base = height, as triangle is an isosceles triangle]
(Base)2=16Base=4cm
In ΔABC, using Pythagoras theorem,
AC2=AB2+BC2=42+42=16+16
AC2=32AC=32cm
[taking positive square root because length is always positive]
Hence, the length of its hypotenuse is 32cm

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