Question

Adjacent sides of a rectangle are in the ratio 5 : 12, if the perimeter of the rectangle is 34 cm, find the length of the diagonal.​

Answer 1

Answer:

Hello!!

Here is the answer.

Given that adjacent sides are in ratio 5:12 and perimeter is 34 cm.

Let the common ratio be k. So, sides will be 5k and 12k.

Now,

P = 2(sum of adjacent sides) 34 = 2 (12k + 5k)

34 = 2 (17k) 34 = 34k

k = 1.

So, sides are

12k 12x1= 12 cm and 5k = 5 cm.

Now, using Pythagoras theorem. Diagonal² = base² + altitude² D² = 12² + 5²

D² =144 + 25 D=√169 = 13 cm.

Hence, the diagonal is 13 cm in length.

Hope It Helps