Question

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
shortest side of the right triangle if the perimeter of the rectangle is 180 cm.
​

Answer 1

Step-by-step explanation:

Let, ️ ABC is a right angled triangle

with <B= 90 °

Let, AB = 3x and BC= 4x

Therefore AC^2 = AB^2 + BC^2 ( Pythagoras Theoram)

=> AC^2 = (3x)^2+(4x)^2

=> AC^2 = 9X^2 + 16X ^2

=> AC^2 = 25 X^2

=> AC = 5X

Therefore In Rectangle ACED

AC = 5X

AE = 4/5 of length

= 4/5×5x

= 4x cm

Therefore Perimeter of ACED

= 2(5X+4X) cm

= 18x cm

According to Question

18x = 180

=> x = 10

Therefore Shortest side of ️ ABC

= 3X cm

= 3× 10

= 30 cm.