Question

the side of a triangle are 16 cm 12 cm and 20 cm what will be the height of the triangle corresponding to the largest side

Answer 1

Answer:

9.6 cm

Step-by-step explanation:

$\text{Sides of triangle (a, b, c) = 16, 12, 20 cm}\\\\\text{Semi-perimeter (s) = } \dfrac{a+b+c}{2} = \dfrac{16+12+20}{2} = \dfrac{48}{2}\\\\\\= 24\\\\\\\therefore \text{Area of triangle } (ar.(\triangle)) = \sqrt{s(s-a)(s-b)(s-c)}\\\\= \sqrt{24(24-16)(24-12)(24-20)}\\\\= \sqrt{24 \times 8 \times 12 \times 4}\\\\= \sqrt{2 \times 2 \times 2 \times 3 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 2 \times 2}\\\\= \sqrt{2^{10} \times 3^2}\\\\= 2^5 \times 3\\\\= 32 \times 3$

$= 96 \: cm^2\\\\\text{Largest side = 20 cm}\\\\\text{Let the height corresponding to the largest side be h.}\\\\\text{Then, area of triangle = } \dfrac{1}{2} \times 20 \times h = 10h\\\\\text{But area of triangle = 96 cm}^2\\\\\therefore \: \: 10 h = 96\\\\\implies h = 96 \div 10 = 9.6 \: cm$

Hope it helps.