Question

Find the area of the triangle two sides of which are 8 cm and 11cm and its perimeter is 32cm

Answer 1

by herons formula

the third side = 32- ( 11+8) = 13

area of the triangle( by herons formula) = √s(s-a)(s-b)(s-c)

s = perimeter/2 = 32/2 = 16

√16(16-11)(16-8)(16-13)

=√16*5*8*3 = 4√5*4*2*3

4*2√15 = 6√15cm²

∴ 6√15cm² is the area of the triangle.

Answer 2

$perimeter \: of \: triangle = 32cm \\ and \: the \: two \: sides \: of \: triangle \: is \: 8cm \: and \: 11cm \: respectively \\ let \: the \: third \: side \: of \: triangle = x \\ so \: perimeter \: of \: triangle \: = side \: + side + side \\ = x + 8 + 11 = 32 \\ x + 8 = 32 - 11 \\ x + 8 = 21$
$x = 21 - 8 \\ x = 13 \\ \\ the \: third \: side \: oftriangle \: is \: 13cm$