Question

The sides of a right angle triangle are in the ratio 3:4. A rectangle is described on its hypotenuse being the longer aide of the rectangle. The breadth of the rectangle is4/5 of its length . Find the shortest side of the right triangle if the perimeter of the rectangle is 180 cm

Answer 1

Hi friend,
Find the solution below!!!

Answer 2

The shortest side of triangle is 30 cm

1) Let the length of the rectangle be x

2)Then the breadth would be 4x/5 as given in the question

3) Total perimeter of the rectangle would be 2(x+4x/5)  = 18x/5

4) Given perimeter is 180 cm. Equating them 18x/5 = 180 cm gives x=50 m

5) Hence the length of rectangle as well as hypotenuse of the triangle is 50 m

6) The ratio of smaller sides is 3:4. Let the sides be 3y and 4y

7) Using Pythagoreas Theorem, the hypotenuse comes out be 5y

8) From hypotenuse = 50, we can find y =10 cm

9) Hence, the smaller sides are 3y and 4y ie 30 cm and 40 cm