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.

Dear Student

Ratio of the adjacent sides of the rectangle = 5 : 12
Let 5x and 12x be the two adjacent sides.
We know that the sum of all sides of a rectangle is equal to its perimeter.
Thus,
5x + 12x + 5x + 12x = 34 cm (given)
34x = 34
x = 34/34
x = 1 cm
Therefore, the adjacent sides are 5 cm and 12 cm respectively.
i.e. l = 12 cm, b = 5 cm
Length of the diagonal = √(l2+ b2)
= √(122+ 52)
= √(144 + 25)
= √169
= 13 cm
Hence, the length of the diagonal is 13 cm.

Thanks