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

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asked Feb 2, 2018 in Class IX Maths by saurav24 Expert (1,427 points)

An isosceles right triangle has area 8 cm2. The length of its hypotenuse is
(a) √32 cm                       
(b) √16 cm                      
(c) √48 cm                    
(d) √24

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1 Answer

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answered Feb 2, 2018 by navnit40 (-4,342 points)

(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.

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