Search 75,791 tutors
FIND TUTORS
Ask a question
0 0

The length of a rectangle is three inches more than the width. The area of the rectangle is 180 inches. Find the width of the rectangle.

Tutors, please sign in to answer this question.

4 Answers

Hey Will -- we could "stair-step" ... 45x40 =180 ... 43x40 is 8 short at 172 ... a 0.2 offset would add 9.4 -- we need about 85% of that ... try 43.17x 40.17= 172.68 +8.634 minus 15% or 1.3 ~ 172.7 +7.3 ~ 180 ==> the 43.17x 40.17 looks really close ... Regards, sir :)

Comments

My apologies, Will -- 40x40 is 1600, not 160 ... PF below has the correct width ==> 12x15

Comment

A=L*W

L=3+W

180= (3+W)W

180=3W+W^2

W^2+3W-180=0

W=(-b +/- (b^2-2ab)^.5)

                2a

The area, A is 180 units.
 
The area A = length times width = L * W
 
but since the length, L, is 3 more than the width, W (or the width plus 3).  So L is bigger than W, right???
 
so use L = (W + 3)
 
now look at the area formula again and use algebra.
 
You can't solve for two different variables with only one equation.  But if you replace the L with (W + 3), you only have one variable and one equation - that we can do!
 
So A = 180 = L * W = (W + 3) * W
 
which is the same as: 180 = W * (W + 3) or simply W(W + 3) = 180
 
next W2 + 3W = 180 (by using the distributive property to multiply)
 
make it into a quadratic equation by subtracting 180 from both sides:
 
now we get W2 + 3W -180 = 0, try to solve by factoring:  (W + ?)(W - ??) = 180
 
 so those question marks will be numbers.  what 2 numbers multiply to -180 and add up to 3?
 
so they are close to each other but one is negative.  
try 18*-10, close but not it.  
 
try 15*something next.  180/15=12
 
so 15*-12 works!
 
so now (W + 15)(W - 12) = 0
 
set each part equal to 0 and solve.  so W + 15 = 0, so W = -15units???  is that realistic?
 
or W - 12 = 0, so W = 12.  That looks good!
 
and since the length is 3 more than that, L = 12 + 3 = 15
 
your answer is W = 12 units and L = 15 units.
 
notice the patterns.   you could use trial and error from the start.  what 2 numbers that are 3 units apart multiply to 180.  you can get it.  but when they get harder or have decimals you'll find that the different algebra formulas and procedures are there to help.
 
Bets, Kim
 
 
A = wl
 
180 = W ( 3+W)
 
 W+3W - 180 =0
 
( W + 15 ) ( W - 12) =0
 
   W = 12 is the only solution.