Question 586543: Find the length and width of the rectangle with the area of 35cm, whose length is x+4cm and width x+2cm
Answer by tw23279(14)   (Show Source):
You can put this solution on YOUR website! At first, you have to recognize that 35cm is the area of a rectangle.
Recall that the area of a rectangle = length x width.
And we have 35cm = (x+4)(x+2) by substituting area with 35cm (it's given) and length with (x+4)cm and width by (x+2)cm (which are also given).
So, foil out (x+4)(x+2) -> x^2 + 2x + 4x + 8 -> x^2 + 6x + 8
So we know that x^2+6x+8 = 35
Move everything to one side so you can solve for x using quadratics.
x^2 + 6x - 27 = 0
Think of two numbers that will add up to 6 and multiply to -27.
So we get that..
(x+9)(x-3) = 0
x = -9 OR x = 3 because remember that if x times y = 0, then x OR y = 0
Since we are looking for the MEASURE of something and that can't be negative.
It will be that x = 3
Length = x+4 = 7 cm
Width = x+2 = 5 cm
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