Find the area (in square cm) of a right angled triangle whose altitude is 7 cm less than its base and its hypotenuse is 17 cm.
60
Let the base of the right-angled triangle be b cm. Altitude = b - 7 cm Hypotenuse = 17 cm By Pythagorean theorem: b² + (b - 7)² = 17² b² + b² - 14b + 49 = 289 2b² - 14b - 240 = 0 b² - 7b - 120 = 0 (b - 15)(b + 8) = 0 b = 15 cm (since b cannot be negative) Altitude = 15 - 7 = 8 cm Area = (1/2) * base * altitude = (1/2) * 15 * 8 = 60 sq cm
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