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Korolek [52]
3 years ago
15

The dimensions of a rectangle are x+3 and x+4. The area of the rectangle is 72. Set up an equation that models this rectangle an

d solve in order to determine the value of x.
Mathematics
1 answer:
vodomira [7]3 years ago
3 0

Answer: x = 5

Step-by-step explanation:

The area of a rectangle is the length times the width. Since the dimensions are given as functions of x, youre going to have to use FOIL to combine them, then set that answer equal to the given value of 72.

l*w = (x+3)*(x+4) = x^2 + 7x +12 = 72

Subtract 72 on both sides. There is a reason why we'll do this instead of subtracting 12. The quadratic formula will help us to solve for x.

x^2 + 7x - 60 = 0

Apply the quadratic formula

\frac{-7 (+/-)\sqrt{7^2-(4)*(1)*(-60} }{2*1} =\frac{-7(+/-)17}{2}

We cant have a negative x value because that would result in negative dimensions and a negative area, which is impossible in this context. So you want to add the 17 instead of subtracting it.

x = 5 and x = -12

An alternate way is just factoring the trinomial to:

(x+12)(x-5) = 0

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Step-by-step explanation:

come on ! based on all the other questions that have been answered AND explained you should be able to find these answers yourself now. what is still unclear ?

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Pythagoras : c² = a² + b²

c is the connection between the 2 points (and which length we need to find).

c = sqrt(a² + b²)

a and b are differences of the x coordinates and the differences of the y coordinates of these 2 points.

a = x1 - x2

b = y1 - y2

this is simply because, when you look at the coordinate grid, these 3 items make a right-angled triangle.

don't worry about any negative values for a and b, as the square eliminates the negative sign.

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we could use Pythagoras again for this, but the end result is so simple, we can skip this.

at the end the coordinates of the midpoint of 2 points (x1, y1) and (x2, y2) are

((x1+x2)/2, (y1+y2)/2)

find the other endpoint (x2, y2), when you have one endpoint (x1, y1) and the midpoint (xm, ym) :

from above you know

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x2 = 2×xm - x1

and in the same way

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and you can read a graph, right ?

if not it is high time to learn that very simple and basic skill :

the x coordinate of a point is how many units right (positive) or left (negative) from the center point it is.

the y coordinate of a point is how many units above (positive) or below (negative) from the center point it is.

the center point is always (0, 0).

so, what else do you need ?

I am very busy explaining things. I should not spend my little time doing the basic calculations for you (that I could train a monkey to do).

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if you run into further problems, please ask me for additional explanations.

8 0
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3 years ago
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Answer:

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Step-by-step explanation:

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Answer:

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We have the formula

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7 0
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