Question

The base of an isoceles triangle is 24 cm and its area is 60 sq. cm. Find its perimeter using Heron's formula.​

Answer 1

Answer:

height

$\bf height = \frac{area}{base} = \frac{60}{24} cm \\ \\ \sf \: perimeter = \frac{1}{2} \times base \times height \\ \\ \sf \implies \frac{1}{2} \times 24 \times \frac{60}{24} = 30cm$

Answer 2

Step-by-step explanation:

$let \: the \: equal \: sides \: be \: x \: metres$

$semiperimeter = \frac{24 + x + x}{2}$

$= \frac{12 + a}{2}$

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

$60 = \sqrt{(x + 12)(x + 12 - x) ( x + 12 - x)(x + 12 - 24)}$

$6 0 = \sqrt{(x + 12)(12)(12)(x - 12)}$

$\sqrt{( {x}^{2} - {12}^{2} )(144)} = 60$

$\sqrt{ {x}^{2} - 144 (144)} =6 0$

${x}^{2} - 144(144) = {60}^{2}$

${x}^{2} + 144 = \frac{3600}{144}$

${x}^{2} + 144 = 25$

${x }^{2} = 25 + 144 \\ = 169 \: \: \: \: \: \\ x = \sqrt{169 } = 13$

$so \\ perimter \: = 24 + 13 +1 3 = 50cm$

hope it's helpful