Question

The height of a triangle is 7 cm less then its base.And its area is 9sq.cm.find the height and base of the triangle

Answer 1

$Let \: the \: base \: of \: a \: triangle (b)= x \:cm\\Height(h) = b - 7 \\= ( x - 7 ) \:cm$

$Area \: of \: the \: triangle (A) = 9 \: cm^{2}$

$\implies \frac{1}{2} \times b h = 9$

$\implies bh = 18$

$\implies x(x-7) - 18 = 0$

$\implies x^{2} - 7x - 18 = 0$

/* Splitting the middle term,we get */

$\implies x^{2} - 9x + 2x - 18 = 0$

$\implies x(x-9)+2(x-9) = 0$

$\implies (x-9)(x+2) = 0$

$\implies x - 9 = 0 \: Or \: x + 2 = 0$

$\implies x = 9 \: Or \: x = -2$

/* We know that, x should not be negative . */

Therefore.,

$Base \: of \: the \: triangle (b) = 9 \:cm$

$Height\: of \: the \: triangle (h)\\ = ( x - 7 )\:cm\\= (9 - 7) \:cm \\= 2\:cm$

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