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The length of a rectangle is eight centimeter less than
twice the width. The area of the rectangle is 24
centimeters squared. Determine the dimensions of the
rectangle in centimeters.

User Koloman
by
4.4k points

1 Answer

7 votes

Answer: The length is 4 centimeters and the width is 6 centimeters.

Explanation:

If the length of the rectangle is eight centimeters less than twice the width then we could represent it by the equation L= 2w - 8 . And we know that to find the area of a rectangle we multiply the length by the width and they've already given the area so we will represent the width by w since it is unknown.

Now we know the length is 2w- 8 and the width is w so we would multiply them and set them equal to 24.

w(2w-8) = 24

2
w^(2) - 8w = 24 subtract 24 from both sides to set the whole equation equal zero and solve. solve using any method. I will solve by factoring.

2
w^(2) - 8w -24 = 0 divide each term by 2.


w^(2) - 4w - 12 = 0 Five two numbers that multiply to get -12 and to -4


w^(2) +2w - 6w - 12 = 0 Group the left hand side and factor.

w(w+2) -6( w + 2) = 0 factor out w+2

(w+2)(w-6) = 0 Set them both equal zero.

w + 2 =0 or w - 6 = 0

-2 -2 + 6 +6

w= -2 or w=6

Since we are dealing with distance -2 can't represent a distance so the wide has to 6.

Now it says that the length is 8 less that twice the width.

So 2(6) - 8 = 12 -8 = 4 So the length in this care is 4.

Check.

6 * 4 = 24

24 = 24

User IEinstein
by
5.4k points