Question

Find the altitude of an isosceles triangle with a base length of 10 centimeters and congruent sides that measure 13 centimeters.

Answer 1

The altitude of an isosceles triangle with a base of 10 cm and sides of 13 cm is found using the Pythagorean theorem and is 12 cm.

Step-by-step explanation:

To find the altitude of an isosceles triangle with a base of 10 centimeters and congruent sides of 13 centimeters, you can use the Pythagorean theorem. First, you split the base into two equal parts of 5 centimeters each, creating two right triangles. In one of these right triangles, one leg is half the base (5 cm), the hypotenuse is the congruent side (13 cm), and the other leg is the altitude you are solving for.

Using the Pythagorean theorem:

a2 + b2 = c2

(altitude)2 + (5 cm)2 = (13 cm)2

(altitude)2 + 25 cm2 = 169 cm2

(altitude)2 = 169 cm2 - 25 cm2

(altitude)2 = 144 cm2

The altitude is the square root of 144 cm2, which is 12 centimeters.