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प्रश्न
The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is ______.
विकल्प
1322 cm2
1311 cm2
1344 cm2
1392 cm2
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उत्तर
The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is 1344 cm2.
Explanation:
The sides of a triangle area = 56 cm, b = 60 cm and c = 52 cm.
So, semi-perimeter of a triangle will be:
`s = (a + b + c)/2`
= `(56 + 60 + 52)/2`
= `168/2`
= 84 cm
Area of the triangle = `sqrt(s(s - a)(s- b)(s - c))` ...[By heron’s formula]
= `sqrt(84(84 - 56)(84 - 60)(84 - 52))`
= `sqrt(84 xx 28 xx 24 xx 32)`
= `sqrt(4 xx 7 xx 3 xx 4 xx 7 xx 4 xx 2 xx 3 xx 4 xx 4 xx 2)`
= `sqrt(4^6 xx 7^2 xx 3^2)`
= 43 × 7 × 3
= 1344 cm2
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