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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 30 inches, and the length of the base is 10 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.

Respuesta :

Perimeter = 78.7 inches
Step-by-step explanation:
From the given question, applying the Pythagoras theorem to one of the congruent triangles formed, we have;
= +
= +
=841 + 81
= 922
hyp =
= 30.3645
The perimeter of the triangle can be determined as;
perimeter = + +
= 30.3645 + 18 + 30.3645
= 78.729
The perimeter of the triangle = 78.7 inches

The perimeter of the triangle is 70.82 inches.

Given as :

The length of the altitude is 30 inches, and

The length of the base is 10 inches

What is right triangle?

Right triangle is defined as a triangle which one angle is a right angle or two sides are perpendicular.

Let, perpendicular = 30 and base = 5

According to Pythagoras theorem,

A right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

perpendicular² + base² = hypotenuse²

Substitute the values,

30² + 5² =  hypotenuse²

900 + 25 =  hypotenuse² or

hypotenuse² = 925

hypotenuse = √925

hypotenuse = 30.41

The perimeter of the triangle can be determined as:

Perimeter of the triangle = l₁ + l₂ + l₃

Perimeter of the triangle = 30.41+ 10 + 30.41

Perimeter of the triangle = 70.82

Hence, the perimeter of the triangle is 70.82 inches.

Learn more about right triangle here:

brainly.com/question/6322314

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