Question

The area of triangle is 80 cm². if the height of the triangle is 6 cm less than its. Base,find the base and its height

Answer 1

$Let \: the \: base \: of \: a \: triangle\:(b) = x \:cm$

$Height (h) = (x-6) \:cm$

$\blue{ Area \: of \: the \: triangle }= 80\:cm^{2}$

$\implies \frac{1}{2} \times b \times h = 80$

$\implies x(x-6) = 2 \times 80$

$\implies x^{2} - 6x - 160 = 0$

$\implies x^{2} - 16x + 10x - 160 = 0$

$\implies x(x-16) + 10(x-16)=0$

$\implies (x-16)(x+10) =0$

$\implies x - 16 = 0 \: Or \: x + 10 = 0$

$\implies x = 16 \: Or \: x = -10$

/* But x should not be negative */

$\red{ 1. Base \: of \:the \: triangle }\green { = 16\:cm }$

$\red{2. Height \: of \:the \: triangle }\\= x - 6 \\= 16 - 6 \\\green { = 6\:cm }$

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