the length of a rectangle is 3 m less than five times the width. the area of the rectangle is 36 m^2. find the dimensions

Question

how to solve it

Answer 1

If the width is W
then the length is 5W-3

W(5W-3)=36
5W²-3W = 36
5W²-3W-36 = 0

Factor by grouping or do the quadratic equation.
Multiply the coefficient of the squared term.. 5..
by the constant ..-36.. 5(-36)=-180
Factors of -180 that add to the coefficient..-3.. of
the W term are 12(-15)
Replace the -3W with -15W + 12W

5W²-15W+12W-36 = 0
5W(W-3) + 12(W-3)=0
(5W+12)(W-3)=0

Either: 5W+12 = 0 or W-3 = 0
5W = -12 0r W=3
W =-12/5

Since W will not be a negative, our width is 3m

The length is 5W-3 = 5(3)-3=15-3 = 12 cm

Hope this helps. Let me know it there are any questions.
Good luck in your class.

Answer 2

Red,

Take the sentence in order:

The length of a rectangle is 3 less than five times the width

                                  L =   -3       +   5W

or L = 5W - 3

 

Now the area of a rectangle is found by A = LW, and A = 36

we can substitute for L in the equation:

 

36 = (5W-3)W

36 = 5W² - 3W

0 = 5W² - 3W - 36      Now factor and apply the zero product rule.

0 = (W-3)(5W+12)

W - 3 = 0        5W + 12 = 0

W = 3               W = -12/5

 

Since we can't have a negative dimension, W = 3.

Plugging into the other equation, L = 5(3) - 3 = 12