Question

The height of a triangle is 3 cm more than the length of the base. If the area of the triangle is 119cm^2 find the height and the length of the base.

Answer 1

`base = 14cm \\ height = 17cm`

Explanation:

Let the length of the base be x

So length of the base = x

height = x +3

`area \: \: of \: \: a \: \: triangle = (1)/(2) * b* h \\ 119 = (1)/(2) * x * (x + 3) \\119 = \frac{ {x}^(2) + 3x }{2} \\ 119 * 2 = {x}^(2) + 3x \\ 238 = {x}^(2) + 3x \\ 0 = {x}^(2) + 3x - 238 \\ {x}^(2) + 3x - 238 = 0 \\ {x}^(2) + 17x - 14x - 238 = 0 \\ x(x + 17) - 14(x + 17) = 0 \\ (x - 14)(x + 17) = 0 \\ \\ x - 14 = 0 \\ x = 14 \\ \\ or \\ x + 17 = 0 \\ x = - 17 \\ \\ length \: \: cannot \: \: be \: \: given \: \: as \: \: a \: \: negative \: \: number \: \: \\ \\ so \\ \: \: base \: = 14cm \\ height = x + 3 \\ = 14 + 3 \\ = 17cm`