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Question
An isosceles right triangle has area 8 cm2. The length of its hypotenuse is ______.
Options
`sqrt(32)` cm
`sqrt(16)` cm
`sqrt(48)` cm
`sqrt(24)` cm
Solution
An isosceles right triangle has area 8 cm2. The length of its hypotenuse is `underlinebb(sqrt(32) cm)`.
Explanation:
Let height of triangle = h
As the triangle is isosceles,
Let base = height = h
According to the question,
Area of triangle = 8 cm2
⇒ `1/2` × Base × Height = 8
⇒ `1/2` × h × h = 8
⇒ h2 = 16
⇒ h = 4 cm
Base = Height = 4 cm
Since the triangle is right angled,
Hypotenuse2 = Base2 + Height2
⇒ Hypotenuse2 = 42 + 42
⇒ Hypotenuse2 = 32
⇒ Hypotenuse = `sqrt(32)`
Hence, the length of its hypotenuse is `sqrt(32)`
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