CBSE Class 7 Answered

Let "a" and "b" be the lengths of the two shorter sides.

The sum is: a + b = 49

so, a = 49 - b

Using Pythagorean Theorem:

perpendicular² + base² = hypotenuse²

(49 - b)² + b² = 41² (by substitution)

2401 - 98b + b² + b² = 1681

2b² - 98b + 720 = 0 (take 2 common from L.H.S)

b² - 49b + 360 = 0

(b - 9)(b - 40) = 0

b = 9 or b = 40

In this case, either solution will do.

If b = 9, then a = 49 - b = 49 - 9 = 40.

Or if b = 40, then a = 49 - b = 49 - 40 = 9.

Thus, one side is 40 inches long, and the other side is 9 inches long.