Question

Find the area of triangle whose perimeter is 180 cm and its two sides are 80 cm and 18 cm calculate the altitude of triangle corresponding to its sortest side

Answer 1

$perimeter = a + b + c$

$18 0 = 80 + 18 + c$

$180 = 98 + c$

$c = 180 - 98$

$c = 82 \: cm$

$s(semi - perimter) = \frac{a + b + c}{2}$

$s = \frac{80 + 18 + 82}{2}$

$s = \frac{180}{2}$

$s = 90 \: cm$

$area = \sqrt{s(s - a)(s - b)(s - c)}$

$= \sqrt{90(90 - 80)(90 - 18)(90 - 82)}$

$= \sqrt{90 \times 10 \times 72 \times 8}$

$\sqrt{3 \times 3 \times 10 \times 10 \times 72 \times 8}$

$= 3 \times 10 \sqrt{9 \times 8 \times 8}$

$= 30 \times 3 \times 8$

$= 90 \times 8$

$= 720 \: cm {}^{2}$

$smallest \: base \: is \: 18 \: cm$

$area \: of \: triangle = \frac{1}{2} \times base \times height$

$720 = \frac{1}{ \cancel2} \times \cancel{18 } ^ {9}\times height$

$height = \frac{720}{9}$

$height = 80 \: cm$