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  • The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is (A) 1322 cm2 (B) 1311 cm2 (C) 1344 cm2 (D) 1392 cm2

The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is

(A) 1322 cm2

(B) 1311 cm2

(C) 1344 cm2

(D) 1392 cm2

Answers (1)

[C]

Given; In \DeltaABC, a = 56 cm, b = 60 cm, c = 52 cm

(Semi perimeter)  S = \frac{a+b+c}{2}

S = \frac{56+60+52}{2}

S = \frac{168}{2}\; = \; 84\; cm

Using Heron’s formula

Area of triangle = \sqrt{S\left ( S-a \right )\left ( S-b \right )\left ( S-c \right )}

= \sqrt{84\left ( 84-56 \right )\left ( 84-60 \right )\left ( 84-52 \right )}

= \sqrt{84\times 28\times 24\times 32}

= \sqrt{7\times 3\times 2\times 2\times 2\times 2\times 7\times 2\times 2\times 6\times 2\times 4\times 4}

= \sqrt{7\times 7\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 4\times 4\times 2}

= 7 × 2 × 2 × 2 × 2 × 4 × 3 = 1344 cm^{^{2}}

Hence area of DABC is 1344 cm^{^{2}}.

Hence option (C) is correct.

 

Posted by

infoexpert21

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