SOLUTION: The length of a rectangle is 5 less than thrice its width. Find the dimensions if the area is 112 squared cm.

Question 154298: The length of a rectangle is 5 less than thrice its width. Find the dimensions if the area is 112 squared cm.
Found 2 solutions by jojo14344, Alan3354:
Answer by jojo14344(1513) (Show Source): You can put this solution on YOUR website!
Remember:
-------------------------------------> working eqn
But , 5 less thrice the width
So substitute,
, distribute

By Quadratic: , , &

, It has 2 values:
--------------------> TO BE USED , WIDTH
-----------------> DON'T USED (-)
Therefore,

In doubt? Go back working eqn:

Thank you,
Jojo
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The length of a rectangle is 5 less than thrice its width. Find the dimensions if the area is 112 squared cm.
---------------------------
L = 3W - 5 (The length of a rectangle is 5 less than thrice its width)
L*W = 112
Sub for L
(3W-5)*W = 112
3w^2 - 5W - 112 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1369 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 7, -5.33333333333333. Here's your graph:

Ignore the negative answer, so W = 7 (the online solver always uses x)
W = 7
L = 3*7 - 5 = 16

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