Math  /  Geometry

QuestionThe length of the longer leg of a right triangle is 19 cm more than five times the length of the shorter leg. The length of the hypotenuse is 20 cm more than five times the length of the shorter leg. Find the side lengths of the triangle.
Length of the shorter leg: \square cm
Length of the longer leg: \square cm Length of the \square cm hypotenuse: 5

Studdy Solution
Verify the solution by calculating the other sides:
- Longer leg: 5x+19=5(13)+19=65+19=84 5x + 19 = 5(13) + 19 = 65 + 19 = 84 cm - Hypotenuse: 5x+20=5(13)+20=65+20=85 5x + 20 = 5(13) + 20 = 65 + 20 = 85 cm
Check using the Pythagorean Theorem:
852=132+842 85^2 = 13^2 + 84^2
7225=169+7056 7225 = 169 + 7056
7225=7225 7225 = 7225
The solution is verified.
The side lengths of the triangle are: - Length of the shorter leg: 13 \boxed{13} cm - Length of the longer leg: 84 \boxed{84} cm - Length of the hypotenuse: 85 \boxed{85} cm

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