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Lubov Fominskaja [6]

3 years ago

6

Find the value of x so the rectangles have the same area

1 answer:

weqwewe [10]3 years ago

7 0

Area of rectangles = width * length.
So x*12 = 12x = area of first rectangle
So 16*(x-2) = 16x -32 = area of second rectangle

The question states to make them equal, so:
first rectangle = second rectangle
12x = 16x -32
Solve for x
-4x = -32
4x = 32
x = 8

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$y = x ^ 2 + 7x + 12\\y = 2x + 8$

Equating both equations we have:

$x ^ 2 + 7x + 12 = 2x + 8\\x ^ 2 + 7x-2x + 12-8 = 0\\x ^ 2 + 5x + 4 = 0$

We must find the solutions, for this we factor. We look for two numbers that, when multiplied, result in 4 and when added, result in 5. These numbers are 4 and 1:

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Then, the factorized equation is of the form:

$(x + 4) (x + 1) = 0$

Thus, the solutions are:

$x_ {1} = - 4\\x_ {2} = - 1$

We look for solutions for the variable "y":

$y_ {1} = 2 (-4) + 8 = -8 + 8 = 0\\y_ {2} = 2 (-1) + 8 = -2 + 8 = 6$

Thus, the system solutions are given by: $(x_ {1}, y_ {1}): (- 4,0)\\(x_ {2}, y_ {2}): (- 1,6)$

ANswer:

$(x_ {1}, y_ {1}): (- 4,0)\\(x_ {2}, y_ {2}): (- 1,6)$

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