Question

ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of $	riangle ADE$ is

Accepted Answer

10. In rectangle $ABCD$, $AD = BC = 45$ cm, and $CD = AB = 56$ cm. Since $E$ is the midpoint of $CD$, $DE = 28$ cm. $	riangle ADE$ is right-angled at $D$. Hypotenuse $AE = \sqrt{45^2 + 28^2} = \sqrt{2025 + 784} = \sqrt{2809} = 53$ cm. Inradius $r$ of right-angled triangle with legs $a, b$ and hypotenuse $c$: $$r = \frac{a + b - c}{2} = \frac{45 + 28 - 53}{2} = \frac{20}{2} = 10	ext{ cm}$$

Incircle Radius of Right Triangle in Rectangle

Explanation

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