Answer:
Dimensions = 7 cm by 20 cm.
Step-by-step explanation:
Let the length and width of the rectangle be L & W respectively.
Given the following data;
Area of rectangle = 140 cm²
L = W - 13
To find the dimensions of the rectangle;
The area of rectangle = L * W
Substituting into the above formula, we have;
140 = L * W
140 = (W - 13) * W
140 = W² - 13W
W² - 13W - 140 = 0
Solving the quadratic equation using factorization method;
Factors are -20 and 7
W² - 20W + 7W - 140 = 0
W(W - 20) + 7(W - 20) = 0
(W - 20)(W + 7) = 0
W - 20 = 0
W = 20
W + 7 = 0
W = -7
Thus, W = 20 or -7
But the width has to be positive, W = 20 centimeters.
Next, to find the length of rectangle
L = W - 13
L = 20 - 13
L = 7 centimeters.
