The ratio of two sides of a rectangle is 3:4 . If its perimeter is 98cm, find the length of each diagonal of the rectangle.

Let the shorter side ( width ) be 3x. Then the longer side ( length ) is 4x, since the sides are in the ratio 3:4.
Perimeter is the sum of all 4 sides i.e 2*(length + width )
Perimeter = 2*(3x+4x)
14x=98
Dividingboth sides by 14,
x=98/14=7
Therefore, width = 3*7 = 21 cm and length = 4*7 = 28 cm.
Width, length and diagonal form a right angled triangle, with the diagonal being the hypotenuse. Using Pythagoras theorem,
Diagonal = (root) width^2+length^2
Diagonal = (root) 21^2+28^2 = (root) 441+784
Diagonal = (root) 1225 = 35 cm

Thankyou