Mathematics, 10.11.2019 05:31 AmityHeart

Asquare and rectangle have equal areas. the length of the rectangle is five inches more than twice the side of the square. the width of the rectangle is 6 inches less than the side of the square. find the length of the side of the square.

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Answer from: stevenssimeon30

Just to make things easier, imagine that x is the length of the side of the square:

According to the information, we can conclude that:

2x + 5 (inches) is the length of the rectangle.

x - 6 (inches) is the width of the rectangle.

Since the areas of the square and the rectangle are the same, we know that:

(2x + 5)(x - 6) = x²

2x² - 12x + 5x - 30 = x²

2x² - 12x + 5x - x² = 30

x² - 7x - 30 = 0

x² + 3x - 10x - 30 = 0

x(x + 3) - 10(x + 3) = 0

(x - 10) (x +3) = 0

Now we can slove each part independently:

x - 10 = 0 or x + 3 = 0

x = 10 or x = -3

Since the length of the side of the square can't be a negative number, we can cancel -3 out and keep 10 only.

So the length of the side of the square is 10 inches.

(This is how I usually do to solve problems of this kind)

Answer from: Quest

the answer is 13

step-by-step explanation:

5*5=25

12*12=144

25+144=169

169^2=13

Answer from: Quest

fabric (square meters) cloaks

7 21

4/3 4

step-by-step explanation:

we are told that harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. first of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

we can see that 3 cloaks can be made from 1 square meter of fabric. now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

therefore, harry will make 21 cloaks from 7 square meters of fabric.

2. let us find how many square meters of fabric will be needed to make 4 cloaks.

first of all we will find fabric needed for 1 cloak by dividing 2 by 6.

we can see that fabric needed for 1 cloak is square meter. now we will multiply by 4 to find fabric needed for 4 cloaks.

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