Question

6. The sides (other than hypotenuse) of a right triangle are in the ratio 3 : 4. A
rectangle is described on its hypotenuse, the hypotenuse being the longer side
of the rectangle. The breadth of the rectangle is four-fifth of its length. Find the
shortest side of the right triangle, if the perimeter of the rectangle is 180 cm.
[Hint. Hypotenuse =
squares of sides = (3x)? +(4x)2 = 25x2 = 5x
4x
sum of
3x ​

Answer 1

In right triangle ABC, ANGLE A= 90°

AB=3X AND AC=4X

BC×BC=AC×AC+AB×AB

BC=5X

IN RECTANGLE BCDE LENGTH BC IS 5X M

BREATH= 4X

P=180

2×L+B=180

X= 10

SHORTEST SIDE = 3×10

30CM