the expressions x-2 and x+3 represent the length and width of a rectangle respectively, if the area of the rectangle is 24 what is the perimeter of the rectangle?

Question

Mathematics

Sandra Peck

7 December, 23:43

the expressions x-2 and x+3 represent the length and width of a rectangle respectively, if the area of the rectangle is 24 what is the perimeter of the rectangle?

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Answers (1)

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Carolyn Caldwell · Answer 1

22

Step-by-step explanation:

The length and width differ by (x + 3) - (x - 2) = 5. The area is the product of length and width, so we can find length and width by looking for factors of 24 that differ by 5. 8 and 3 are such factors.

The length is 3 and the width is 8, so the sum of length and width is 11. The perimeter is twice that value, so the perimeter is 22.

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x=5

If you write the quadratic equation, (x-2) (x+3) = 24, you find there is a negative solution, too. That is x=-6, giving dimensions of - 8 and - 3. That is not a useful solution.

As is often the case, you can go directly to the solution by making use of your knowledge of times tables. You don't need the quadratic equation to find the answer to this question.