# The length of the rectangle is 5cm less than thrice its width. Find the dimensions of the rectangle if its area is 112cm²?

##### 1 Answer

Length:

Width:

#### Explanation:

First, start by writing the formula for the area of a rectangle of width

#color(blue)(A = l * w)#

Now, you know that if you **triple** the rectangle's width and subtract 5 cm from the result, you get the rectangle's length.

This means that you can write

#l = 3 * w - 5#

Since you know that the area of the rectangle is equal to

#(3w - 5) * w = 112#

#3w^2 - 5w = 112#

#3w^2 - 5w - 112 = 0#

Use the *quadratic formula* to find the two solutions to this quadratic equation

#w_(1,2) = ((-5)) +- sqrt((-5)^2 - 4 * 3 * (-112))/(2 * 3)#

#w_(1,2) = (5 +- sqrt(1369))/6#

#w_(1,2) = (5 +- 37)/6#

Since *negative solution* will have no physical significance. This means that the only valid solution to this quadratic is

#w = (5 + 37)/6 = 42/6 = color(green)("7 cm")#

The length of the rectangle will be

#3 * 7 - 5 = 21 - 5 = color(green)("16 cm")#