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 △ADE is
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 △ADE is
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 △ADE is
Options
Answer: 10
Explanation:
Rectangle ABCD: AB = CD = 56, BC = AD = 45. E is midpoint of CD, so DE = 28. △ADE has sides: AD = 45, DE = 28, AE = √(45² + 28²) = √(2025 + 784) = √2809 = 53. Semi-perimeter s = (45 + 28 + 53)/2 = 63. Area = (1/2) × AD × DE = (1/2) × 45 × 28 = 630. Inradius r = Area/s = 630/63 = 10 cm.
Explanation:
Rectangle ABCD: AB = CD = 56, BC = AD = 45. E is midpoint of CD, so DE = 28. △ADE has sides: AD = 45, DE = 28, AE = √(45² + 28²) = √(2025 + 784) = √2809 = 53. Semi-perimeter s = (45 + 28 + 53)/2 = 63. Area = (1/2) × AD × DE = (1/2) × 45 × 28 = 630. Inradius r = Area/s = 630/63 = 10 cm.
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