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
Sep 6, 2015

Answer:

Length: #"16 cm"#
Width: #"7 cm"#

Explanation:

First, start by writing the formula for the area of a rectangle of width #w# and length #l#

#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 #"112 cm"""^3#, you can write a second equation using #l# and #w#

#(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 #w# represents the width of the rectangle, the 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")#