Question

The sides of a Δ are 7 cm, 24 cm and 25 cm. Its area is :

Answer 1

Answer:

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Step-by-step explanation:

$so \: here \\ for \: a \: certain \: triangle \: , given \: sides \: are \\ \: 24.cm,7.cm \: and \: 25 \: cm \\ \\ let \: then \\ a = 24.cm \\ b = 7.cm \\ c = 25.cm \\ \\ so \: thus \: then \\ semiperimeter \: (s) = \frac{a + b + c}{2} \\ \\ = \frac{25 + 24 + 7}{2} \\ \\ = \frac{56}{2} \\ \\ s= 28.cm$

$so \: by \: herons \: formula \\ we \: get \\ \\ A(△) = \sqrt{s (s - a)(s - b)(s - c)} \\ \\ = \sqrt{28(28 - 7)(28 - 24)(28 - 25)} \\ \\ = \sqrt{28 \times 21 \times 4 \times 3} \\ \\ = \sqrt{(7 \times 4) \times (7 \times 3) \times (2 \times 2) \times 3} \\ \\ = \sqrt{(7 \times 2 \times 2) \times (7 \times 3) \times (2 \times 2) \times 3} \\ \\ = \sqrt{(7) {}^{2} \times (2 \times 2) {}^{2} \times (3) {}^{2} } \\ \\ = 7 \times 4 \times 3 \\ \\ = 28 \times 3 \\ \\ A(△)= 84. \: unit {}^{2}$