MATH SOLVE

2 months ago

Q:
# A rectangle has a length, 3x+7, and a width of x+5. The area of the rectangle is 128 square inches. What is the length of the rectangle in inches?

Accepted Solution

A:

First, we know the formula for area is:

Area = Length* Width

Therefore, 128 = (3x+7)(x+5)

We can use the F.O.I.L method to multiply

- First: (3x *x )= 3x²

-Outer: (3x*5) = 15x

-Inner: (7*x) = 7x

-Last: (7*5) = 35

Now we add the sum → 3x² + 15x + 7x + 35 → 3x² + 22x + 35

3x²+ 22x + 35 = 128

3x²+ 22x -93 = 0

Now you have to factor to solve for the x value.

(3x+31)(x−3)

x = 3 & x = -31/3

The negative value is eliminated because u can't have a negative length.

The length is 3x+7

L= 3(3) +7

L= 9+7

L= 16

Area = Length* Width

Therefore, 128 = (3x+7)(x+5)

We can use the F.O.I.L method to multiply

- First: (3x *x )= 3x²

-Outer: (3x*5) = 15x

-Inner: (7*x) = 7x

-Last: (7*5) = 35

Now we add the sum → 3x² + 15x + 7x + 35 → 3x² + 22x + 35

3x²+ 22x + 35 = 128

3x²+ 22x -93 = 0

Now you have to factor to solve for the x value.

(3x+31)(x−3)

x = 3 & x = -31/3

The negative value is eliminated because u can't have a negative length.

The length is 3x+7

L= 3(3) +7

L= 9+7

L= 16