Question

The sides other than hypotenuse) of a right angled 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 reciangle is four-fifth of its length. Find the shortest side of the right-triangle, if the perimeter
of the rectangle is 180 cm.​

Answer 1

Answer:

30cm

Step-by-step explanation:

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.