Question
In a right-angled triangle, the legs are in the ratio
3:4, and the hypotenuse is 25 cm. Find the perimeter of the triangle.Solution
Let the legs of the triangle be 3x and 4x, and the hypotenuse is 25 cm. By Pythagoras’ theorem: (3x)² + (4x)² = 25² 9x² + 16x² = 625 25x² = 625 x² = 25 x = 5. Therefore, the lengths of the legs are 3x = 15 cm and 4x = 20 cm. The perimeter of the triangle = 15 + 20 + 25 = 60 cm.
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