Which statement is true of a rectangle that has an area of 4x2 + 39x – 10 square units and a width of (x + 10) units?

The rectangle is a square.
The rectangle has a length of (2x – 5) units.
The perimeter of the rectangle is (10x + 18) units.
The area of the rectangle can be represented by (4x2 + 20x – 2x – 10) square units.

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Answer:

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C.) The perimeter of the rectangle is (10x + 18) units.

Step-by-step explanation:

The perimeter of the rectangle is (10x + 18) units.

Area and perimeter of a rectangle

Area of rectangle = length * breadth

Given the following

Area = 4x^2 + 39x – 10

Expand the expression

Area = 4x^2 + 40x - x - 10

Area = 4x(x+10)-1(x+10)

Area = (4x-1)(x+10)

Hence the width of the rectangle is 4x - 1

Perimeter = 2(L + w)

P = 2(4x-1+x+10)
P = 2(5x +9)
P = 10x + 18

The perimeter of the rectangle is (10x + 18) units.

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