The Length Of A Rectangle Is 5 Inches More Than Twice A Number Answer

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The Length Of A Rectangle Is 5 Inches Answer & Explanation

MATHEMATICS QUESTION – The length of a RECTANGLE is 5 inches more than twice a number. The width is 4 inches less than the same number. If the area of the rectangle is 15, find the number.

This could be solved easily! The answer to the question is -1 and 5/2. Here’s the step-by-step solution:

The Length Of A Rectangle Is 5 Inches More Than Twice A Number Answer
  • Length = 5 inches more than twice a number
    • 2x + 5
  • Width = 4 inches less than the same number
    • 4 -x
  • Area = L x W
    • 15 = (2x + 5) x (4 – x)

The question now is to find the value of x. First, we need to expand the equation above to get:

15 = (2x+15)(4-x)
15 = 8x – 2x^2 + 20 – 5x
15 = 3x – 2x^2 + 20
15 – 3x + 2x^2 – 20 = 0
-5 – 3x+ 2x^2 = 0
2x^2 + 2x – 5x – 5 = 0

From here, we could solve for the zeroes:

2x(x + 1) – 5(x+1) = 0
(x+1)(2x-5) = 0
Therefore, the possible answers are (x = -1) and (x = 5/2).

To check, we simply need to substitute the values we got with the original formula to verify it.

For x = – 1

15 = (2( - 1) + 5)(4 - ( - 1) \\ \\ 15 = ( - 2 + 5)(4 + 1) \\ \\ 15 = (3)(5) \\ \\ 15 = 15

For x = 5/2

15 = (2( \frac{5}{2} ) + 5)(4 - \frac{5}{2} )\\ \\ 15 = (5 + 5)( \frac{3}{2} ) \\ \\ 15 = (10)( \frac{3}{2} ) \\ \\ 15 = \frac{10 \times 3}{2} \\ \\ 15 = \frac{30}{2} \\ \\ 15 = 15

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