The height of a triangle is $3 \mathrm{~cm}$ more than the length of the base. If the area of the triangle is $90 \mathrm{~cm}^{2}$, find the height and length of the base.
A) height: $16 \mathrm{~cm}$, base: $11 \mathrm{~cm}$
B) height: $15 \mathrm{~cm}$, base: $12 \mathrm{~cm}$
C) height: $12 \mathrm{~cm}$, base: $9 \mathrm{~cm}$
D) height: $14 \mathrm{~cm}$, base: $11 \mathrm{~cm}$

Question

Quizplus · Accepted Answer

The area of a triangle is given by $\frac{1}{2} \times \text{base} \times \text{height}$. Let the base be $x$, then the height is $x + 3$. The equation becomes $\frac{1}{2} \times x \times (x + 3) = 90$. Solving this gives $x = 12$ (base) and $x + 3 = 15$ (height).

The Height of a Triangle Is 3 cm3 \mathrm{~cm}3 cm More Than the Length of the Base

The Height of a Triangle Is $3 \mathrm{~cm}$ More Than the Length of the Base