A rectangular carpet has an area of 120 sq. metres and a perimeter of 46 metres. What is the length of the diagonal?

Question: A rectangular carpet has an area of 120 sq. metres and a perimeter of 46 metres. What is the length of the diagonal?

Solution:
Let the length and breadth of the rectangle be x and y metres.

given 2(x + y) = 46
x + y = 23
x = 23 - y

and,
xy = 120
(23 - y) y = 120
23y - y² = 120
y² - 23y + 120 = 0
y² - 15y - 8y + 120 = 0
y(y - 15) - 8(y - 15) = 0
(y - 15) (y - 8) = 0
y = 15 or, 8

∴ length, x = 15 and breadth, y = 8

so, the diagonal is = √{(15)² + (8)²}
= √289
= 17