Question

10 multiple choice 1 point an isosceles triangle has a base with length 15 inches and two congruent sides with lengths of 12 inches each. find the height of the triangle. (round your answer to the nearest tenth of an inch) 9.7 inches 9.4 inches 8.8 inches 9.1 inches 10.0 inches

Explanation:

Step1: Divide the isosceles triangle

The height of an isosceles triangle divides it into two right - triangles. The base of each right - triangle is $\frac{15}{2}=7.5$ inches (half of the base of the isosceles triangle), and the hypotenuse is 12 inches.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem for a right - triangle is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. Let the height be $h$. We have $h=\sqrt{12^{2}-7.5^{2}}$.
First, calculate $12^{2}=144$ and $7.5^{2}=56.25$. Then $12^{2}-7.5^{2}=144 - 56.25=87.75$.
So, $h=\sqrt{87.75}\approx9.4$ inches.

Answer:

9.4 inches