A triangle has an area of 45 square inches. The height of the triangle is 2 $\frac { 1 } { 2 }$ times its base. Find the height of the triangle.
A)11 inches
B)30 inches
C)15 inches
D)21 inches
E)90 inches

Question

Quizplus · Accepted Answer

Let the base of the triangle be $b$. Then the height is $2\frac{1}{2}b = \frac{5}{2}b$. The area of the triangle is $\frac{1}{2}bh = \frac{1}{2}(b)\left(\frac{5}{2}bight) = \frac{5}{4}b^2$. We are given that this area is 45, so $\frac{5}{4}b^2 = 45$ and $b^2 = 36$. Since $b$ is a length, $b>0$ and we have $b=6$. So the height of the triangle is $\frac{5}{2}b = \frac{5}{2}(6) = \boxed{	extbf{(C) } 15	ext{ inches}}$.

A Triangle Has an Area of 45 Square Inches 12\frac { 1 } { 2 }21​

A Triangle Has an Area of 45 Square Inches $\frac { 1 } { 2 }$