Final answer:
To find the inscribed circle radius in an isosceles triangle with a 10 cm base and a 13 cm leg, use the Pythagorean Theorem to find the height, calculate the area, compute the semiperimeter, and apply the formula for an inscribed circle radius, resulting in approximately 3.33 cm.
Step-by-step explanation:
To find the radius of a circle inscribed in an isosceles triangle, where the length of the base is 10 cm and the length of the leg is 13 cm, you can follow these steps:
- Use the Pythagorean Theorem to calculate the height of the triangle. Let's label the height as h, the base as b, and the leg as l. Since the triangle is isosceles, the base will be divided into two equal parts of 5 cm each.
- h can be found by: h = √(l² - (b/2)²) = √(13² - 5²) = √(169 - 25) = √144 = 12 cm.
- Calculate the area (A) of the triangle using the formula A = 1/2 × base × height. The area is thus 1/2 × 10 cm × 12 cm = 60 cm².
- The semiperimeter (s) of the triangle is (10 cm + 13 cm + 13 cm) / 2 = 18 cm.
- Now use the formula for the radius (r) of an inscribed circle, which is r = A / s. Here, r = 60 cm² / 18 cm = 3.33 cm.
So, the radius of the inscribed circle is approximately 3.33 cm.