Solve the problem.
-The height of a triangle is $3 \mathrm{~cm}$ more than the length of the base. If the area of the triangle is $65 \mathrm{~cm}^{2}$, find the height and length of the base.
A) height: $13 \mathrm{~cm}$; base: $10 \mathrm{~cm}$
B) height: $14 \mathrm{~cm}$; base: $9 \mathrm{~cm}$
C) height: $12 \mathrm{~cm}$; base: $9 \mathrm{~cm}$
D) height: $10 \mathrm{~cm}$; base: $7 \mathrm{~cm}$

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 $x$ cm. Then, the height is $x + 3$ cm. The area is $65 \text{ cm}^2$, so $ \frac{1}{2} \times x \times (x + 3) = 65 $. Solving this quadratic equation gives $x = 10$ cm for the base, and thus the height is $13$ cm.

Solve the Problem 3 cm3 \mathrm{~cm}3 cm More Than the Length of the Base

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