Question

In a triangle ABC, AB=AC=x, BC=10 and the area of the triangle is 60cm^2.Find x

Answer 1

Answer:

AB = AC = x

area = 60 cm^2

By heron's formula ,

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

$s = \frac{a + b + c}{2}$

In ∆ ABC

$s = \frac{x + x + 10}{2}$

$s = \frac{x}{5}$

Therefore

$area \: of \: triangle \: \sqrt{(x + 5)(x + 5 - x)( x + 5 - x)(x + 5 - 10)}$

$60 = \sqrt{(x + 5)25( x - 5)}$

$3600 = 25( {x}^{2} - 25)$

${x}^{2} = 169$

$so \: ...x = 13cm$

THEREFORE THE VALUE OF X IS 13 cm

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