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Question
Area of a right-angled triangle is 30 cm2. If its smallest side is 5 cm, then its hypotenuse is ______.
Options
14 cm
13 cm
12 cm
11 cm
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Solution
Area of a right-angled triangle is 30 cm2. If its smallest side is 5 cm, then its hypotenuse is 13 cm.
Explanation:
Given, area of a right-angled triangle = 30 cm2
And smallest side i.e. base = 5 cm
We know that,
Area of right angled triangle = `1/2` × Base × Height
∴ 30 = `1/2` × 5 × Height
⇒ Height = `(30 xx 2)/5`
⇒ Height = 12 cm
Now, according to Pythagoras theorem,
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
⇒ (Hypotenuse)2 = (12)2 + (5)2 ...[∵ Height = Perpendicular]
⇒ (Hypotenuse)2 = 144 + 25
⇒ (Hypotenuse)2 = 169
⇒ Hypotenuse = `sqrt(169)`
⇒ Hypotenuse = 13 cm
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