Question

in a trangle abc, ab=15cm,bc=13cm and ac=14cm. Find its area and hence it's altitude on ac

Answer 1

S = (15 + 13 + 14)/2 = 21

Now apply herons formula

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

$\sqrt{21(21 - 15)(21 - 13)(21 - 14)}$

$\sqrt{21 \times 6 \times 8 \times 7}$

$\sqrt{3 \times 7 \times 3 \times 2 \times 2 \times 2 \times 2 \times 7}$

$area = 84cm {}^{2}$

Area = 1/2 × b × h

84 = 1/2 × 14 × h

(84 × 2)/14 = h

h = 12 cm


Thanks