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 13 inches, and the length of the base is 8 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch

Answer 1

Answer:

12.2 inches

Step-by-step explanation:

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 5 inches, and the length of the base is 2 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.

Answer 2

The length of the sides of the isosceles triangle can be found from the

given altitude and the length of the base.

• The perimeter of the triangle is approximately 35.2 inches.

Reasons:

The given parameter are;

The triangle is an isosceles triangle

The altitude cuts the base into two

Length of the altitude, h = 13 inches

Length of the base of the triangle, l = 8 inches

Required:

Find the perimeter of the triangle.

Solution:

By using the Pythagorean theorem, we have;

Length of one of the isosceles sides of the triangle which is an hypotenuse

side of the right triangle formed by the altitude, R, is given as follows;

$\displaystyle R = \mathbf{\sqrt{ h^2 + \left(\frac{l}{2} \right)^2}}$

Therefore;

$\displaystyle R = \sqrt{ 13^2 + \left(\frac{8}{2} \right)^2} = \mathbf{ \sqrt{ 13^2 + 4^2}} =\sqrt{185}$

R = √(185) inches

Therefore, the length of the other hypotenuse side = R = √(185) inches

On the original triangle, the sides are; R, R, and l

Which gives;

The perimeter of the triangle, P = R + R + l = 2·R + l

Therefore;

P = 2 × √(185) + 8 ≈ 35.2

The perimeter of the triangle, P ≈ 35.2 inches.

Learn more about Pythagorean theorem here:

https://brainly.com/question/2514956