Question

an altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. as a result, the altitude cuts the base into two equal segments. the length of the altitude is 30 inches, and the length of the base is 10 inches. find the triangle’s perimeter. round to the nearest tenth of an inch.

Explanation:

Step1: Find half of the base

The base is 10 inches, so half of it is $\frac{10}{2} = 5$ inches.

Step2: Use Pythagorean theorem to find leg length

Let the leg length be $l$. The altitude is 30 inches (one leg of right triangle), half - base is 5 inches (other leg of right triangle). By Pythagorean theorem $l=\sqrt{30^{2}+5^{2}}=\sqrt{900 + 25}=\sqrt{925}\approx30.41$ inches.

Step3: Calculate the perimeter

The isosceles triangle has two equal legs and a base. Perimeter $P=2l + 10$. Substitute $l\approx30.41$: $P=2\times30.41+10=60.82 + 10=70.82\approx70.8$ inches.

Answer:

70.8 inches