Question

The side other than hypotenuse of a right triangle are in the ratio 3 is to 4 a rectangle is described on its hypotenuse the hypotenuse begin the longer side of the rectangle the breadth of the rectangle is 4.5 of its length find the shortest side of the right triangle if the perimeter of the rectangle is a 180 cm

Answer 1

let the sides be 3a and 5a

by pythagoreas theorem

3a^2+4a^2=x^2

x=5a

therefore lenght of hypotenuse is 5a

length of rectangle l=5a

breadth b=4.5l

4.5l*2+5a*2=180

45a+5a=180

50a=180

a=3.6cm

therefore shortest side is 3a=3.6*3=10.8

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