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Paladinen [302]
2 years ago
14

The length of a rectangle is 5 cm more than twice a number. the width is 4cm less than the same number. if the area of the recta

ngle is 15cm2, find the number
​
Mathematics
1 answer:
lana [24]2 years ago
7 0
A = Lw (area of rectangle is length times width)
A = 15 (Area is 15)
L = 2x + 5 (length is 2 times a number plus another 5)
w = x - 4 (width is 4 less than that number

Plug in the values:
15 = (2x + 5)(x - 4)
FOIL
15 = 2x2 - 8x + 5x - 20
simplify:
15 = 2x2 - 3x - 20
Subtract 15
0 = 2x2 - 3x - 35
Factor out the quadratic. We know that one number has to be 7 and the other 5 so that they multiply together to make 35, and that one of them has to be negative so that it's actually -35.
That means we have m * n = -35
We also need it set up so that so that 2m + n = -3:
2 * -5 + 7 = -3
0 = (2x + 7)(x - 5)
So:
0 = 2x + 7, or 0 = x - 5
x = -7/2 or 5
We cannot have a negative length, so x = 5

Check:
15 = (2 * 5 + 5) (5 - 4)
15 = 15 * 1
15 = 15
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General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

Step-by-step explanation:

<u>Step 1: Define</u>

p/5 = -32

<u>Step 2: Solve for </u><em><u>p</u></em>

  1. Multiply 5 on both sides:                     p = -160
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