Question

Find the area of a triangle having perimeter 32cm. One of its side is equal to 11cm and difference of the other two is 5

Answer 1

let others side be x
and other is x - 5

perimeter = sum of all sides

$32 =11 + x + x - 5 \\ 32 = 6 + 2x \\ 2x = 32 - 6 \\2 x = 26 \\ x = 13$
1st side = 13 cm
2nd = 13 - 5 = 8cm

$s = \frac{a + b + c}{2} \\ s = \frac{11 + 13 + 8}{2} \\ s = \frac{32}{2} \\ s = 16$
$area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} \\ \sqrt{16(16 - 11)(16 - 13)(16 - 8)}$