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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

Sagot :

xhiyazx

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.

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;

[tex]\displaystyle R = \mathbf{\sqrt{ h^2 + \left(\frac{l}{2} \right)^2}}[/tex]

Therefore;

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

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

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