Answer:
Length of the shorter side = -10 units or 22 units.
Explanation:
Let x = length of the longer side of the rectangle
Let y = length (width or breadth) of the shorter side of the rectangle
Given the following data;
x = y + 12
Area = 220 units
We know that the area of a rectangle is given by the formula;
[tex] Area, A = length * width[/tex]
Substituting into the equation, we have;
[tex] 220 = (y + 12) * y[/tex]
[tex] 220 = y^{2} + 12y[/tex]
Rearranging the equation, we have;
[tex] y^{2} + 12y - 220 = 0[/tex]
Solving the quadratic equation by factorization, we have;
Factors are = -10 and 22
[tex] y^{2} - 10y + 22y - 220 = 0[/tex]
[tex] y(y - 10) + 22(y - 10) = 0[/tex]
[tex] (y - 10)(y + 22) = 0[/tex]
Therefore, y = 10 units or -22 units
To find the value of x;
When y = 10 units
x = y + 12
Substituting into the equation;
x = 10 + 12 = 22
x = 22
When y = -22 units
x = y + 12
Substituting into the equation;
x = -22 + 12 = -10
x = -10
Check;
When x = 22 and y = 10
A = L * W = 22 * 10 = 220 units
When x = -10 and y = -22
A = L * W = -10 * -22 = 220 units
