If the perimeter of a certain rectangle is 50 units and its area is 150 sq. units, then how many units is the length of its shorter side?

Let the side of rectangle be x and y.

Perimeter of a rectangle = 50 units

2(x + y) = 50

x + y = 25 ---(1)

Area = 150

xy = 150 

x = 150/y

From equation (1),

(150/y) + y = 25

$$150 + y^2 = 25y$$

$$ y^2 - 25y + 150 = 0$$

$$ y^2 - 15y - 10y + 150 = 0$$

$$ y(y - 15) - 10(y - 15) = 0$$

$$(y - 15)(y - 10) = 0$$

y = 15 or y = 10

From equation (1),

When y = 15

15 + x = 25

x= 10

When y = 10

10 + x = 25

x= 15

Sides are 10 and 15.

Length of shorter side =10