SOLUTION: Find the dimensions of a rectangle with a perimeter of 112 cm if the length is 4 cm less than four times the width.

Question 310984: Find the dimensions of a rectangle with a perimeter of 112 cm if the length is 4 cm less than four times the width.
Answer by PRMath(133) (Show Source): You can put this solution on YOUR website!
Find the dimensions of a rectangle with a perimeter of 112 cm if the length is 4 cm less than four times the width.

Ok... you have to first tell yourself that a perimeter is the sum of the measurements of all four sides of the rectangle. In other words, you add all four sides and voila, you have the perimeter.

In a rectangle, tho, you have TWO lengths and TWO widths. The equation to find the perimeter, then,if we use "L" for Length and "W" for Width is:

L + L + W + W = Perimeter

Now this problem tells us that the perimeter is 112 cm. At first then, we can set up this equation: L + L + W + W = 112. We don't know, tho, the lengths and the widths - or do we?

WELL.. the problem says this: the length is 4 cm less than four times the width. All you have to do is write that information in an equation form. Break down what you are given and see what you come up with:

The Length: L
is: =
4 cm less than 4 times the width: 4w - 4 <---See how this is 4 cm less than four times the width?

Our equation then is: L = 4w - 4 and you can PLUG this info into the equation we started with, like this:

L + L + W + W = 112
4w - 4 + 4w - 4 + W + W = 112 (see where I replaced "L" with 4w - 4? Now combine like terms, by adding the "Ws" and the numbers:

10W - 8 = 112 (now add 8 to both sides to start to isolate the w)
10W = 112 + 8
10w = 120 (now divide both sides by 10 to further isolate the w)
w = 12

SO --- now we know that w = 12. We can just plug this info into what we were told about the length, which was: the length is 4 cm less than four times the width OR as we wrote it: L = 4w - 4

SO let's use that equation and plug in our info:

L = 4w - 4
L = 4(12) - 4 (See where we plugged "12" in where the "w" was?)
L = 48 - 4
L = 44

Now we know that the width is 12 and the length is 44. Does that work out in what we know to be the perimeter of the shape? We were told the perimeter was 112 cms, so, let's test our numbers out:

L + L + W + W = 112
44 + 44 + 12 + 12 = 112

YAY! It works out! Sooooo our length is 44 cm and our width is 12 cm.

I hope this was helpful. :-)

RELATED QUESTIONS
Find the dimensions of a rectangle with a perimeter of 90 cm if the length is 5 cm less... (answered by checkley77)

Find the dimensions of a rectangle with a perimeter of 90 cm if the length is 5 cm less... (answered by unlockmath)

Find the dimensions of a rectangle with a perimeter of 34 cm if the length is 4 cm less... (answered by checkley77)

the perimeter of a rectangle is 112 cm. the length is 6 cm greater than 4 times the... (answered by TimothyLamb)

Find the dimensions of a rectangle with a perimeter of 42 cm if the length is 7 cm less... (answered by solver91311)

The length of a rectangle is 4 cm less than 3 times the width. if the perimeter is 88 cm, (answered by rfer)

The length of rectangle is 3 cm less than four times its width. If the perimeter is 34... (answered by solver91311)

The length of a rectangle is 5 cm less than than thrice its width. find the dimensions of (answered by macston)

The length of a rectangle is 5 cm less than three times its width. If the perimeter is 70 (answered by Maths68)