Question

The length of a rectangle is 13 centimeters less than three times its width. Its area is 56 square centimeters. Find the dimensions of the rectangle. Use the​ formula, area=length*width.

Answer 1

Answer:

Area = length  x width

Area = (3width - 13) x width

Area = 3 width^2 -13width

56 = 3width^2 -13 width

Width = 7

Length = (3 *7) -13 = 8

Step-by-step explanation:

Answer 2

Answer:

The dimensions of the rectangle are 8 by 7 centimeters.

Step-by-step explanation:

The length of a rectangle is 13 centimeters less than three times its width. In other words:

$\ell = 3w-13$

Given that the area of the rectangle is 56 square centimeters, we want to determine its dimensions.

Recall that the area of a rectangle is given by:

$A = w \ell$

Substitute in known values and equations:

$(56)=w(3w-13)$

Solve for w. Distribute:

$3w^2-13w=56$

Isolate the equation:

$3w^2-13w-56=0$

Factor. We want to find two numbers that multiply to 3(-56) = -168 and that add to -13.

-21 and 8 suffice. Hence:

$3w^2 - 21w + 8w - 56 = 0 \\ \\ 3w(w-7) + 8(w-7) = 0 \\ \\ (3w+8)(w-7) = 0$

Zero Product Property:

$3w+8=0\text{ or } w-7=0$

Solve for each case:

$\displaystyle w = -\frac{8}{3} \text{ or } w=7$

Since the width cannot be negative, we can ignore the first solution.

Therefore, the width of the rectangle is seven centimeters.

Thus, the length will be:

$\ell = 3(7) - 13 = 8$

Thus, the dimensions of the rectangle are 8 by 7 centimeters.