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The dimensions of a rectangle can be given by x+7 and x+2. If the area of the rectangle is 66 square inches, what are the dimensions of the rectangle?

Respuesta :

mrworldwide

to solve  for the dimensions (x+7)(x+2)=66,

we can first use the foiling method to simplify the left side.

x^2 + 2x + 7x + 14 = 66

x^2 + 9x + 14 = 66

now, subtract 66 from both sides.

x^2 + 9x - 52 = 0

now, split this into two parentheses.

(x + 13)(x - 4)

since the root of -13 would give you negative values, x=4. This means that the dimensions of the rectangle are 11 and 6.

MrRoyal

The dimensions of the rectangle is 11 by 6 inches

How to determine the dimensions?

The dimensions are given as:

x + 7 and x + 2

The area is given as:

Area = 66

The area of a rectangle is:

Area = Length * Width

So, we have:

(x + 7) * (x + 2) = 66

Express 66 as 11 * 6

(x + 7) * (x + 2) = 11 * 6

By comparison, we have:

x + 7 = 11 and x + 2 = 6

Solve for x

x = 4 and x = 4

Substitute 4 for x in x + 7 and x + 2

x + 7 = 4 + 7 = 11

x + 2 = 4 + 2 = 6

Hence, the dimensions of the rectangle is 11 by 6 inches

Read more about areas at:

https://brainly.com/question/24487155

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