Question

the sides (other than hypotenuse) of a right triangle are in ratio 3:4 . A rectangle is described on its hypotenuse,the hypotenuse beingtye longer side of the rectangle. the breadth of rectangle is 4/5 of its length. find the shortest side of the right triangle if the perimeter of the rectangle is 180cm.

Answer 1

In right triangle ABC, angle A= 90°

AB:AC=3:4

Therefore, AB=3x and AC=4x

By pythogorus theroum

BC=√AC×AC+AB×AB

BC=5x

Now, In rectangle BCDE , Length =BC=5x


Since, BC= 4/5×5x=4x

But,

Perimeter = 180cm


2×(5x+4x)=180

x=10

since, the shortest side of right ∆ ABC=3x
= 3×10
=30cm. Ans.

Answer 2

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