Question

10. 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
4
of its length. Find the
5
side of the rectangle. The breadth of the rectangle is
shortest side of the right triangle if the perimeter of the rectangle is 180 cm.
​

Answer 1

Answer:

Let the sides AB and BC of right triangle in figure are 4x and 3x respectively.

 

then side AC = begin mathsize 12px style square root of open parentheses 4 x close parentheses squared plus open parentheses 3 x close parentheses squared end root space equals space 5 x end style

breadth AE of rectangle = (4/5) of (5x) = 4x.

 

perimeter of rectangle = 2(4x+5x) = 180 cm.........(1)

From eqn.(1), we get x = 10 cm.

 

shortest side of triangle = 3x = 3×10 = 30 cm

Step-by-step explanation: