Question

If a rectangle has a perimeter of 70, a length of x and a width of x - 9, find the value of the length of the rectangle.

Answer 1

The length x = 22

Explanation:

Notice that we are not given the length and the with of the rectangle. Therefore they are both UNKNOWNS which we can identify as follows:

The length with the letter x -as given in the problem,

and the width with the expression given to us (which relates to the length x): x-9

Now let's write the expression for the perimeter of a rectangle (which consist of the addition of all its four sides). Two of the rectangle's sides are of length "x" (the rectangle's length) and the other two are of length "x-9" (the rectangle's width). So the total addition of these four sides can be written as:

Perimeter = x + x + (x-9) + (x-9)

Removing the parentheses (grouping symbols) so we can combine all like terms:

x + x + x - 9 + x - 9 = 4 x -18

Now we use the info given to us regarding the actual value for the perimeter (70), and complete an equation for the perimeter as:

Perimeter = 70

4 x - 18 = 70

Now solve for the unknown "x" by isolating it on one side of the equal sign:

4 x = 70 + 18

4 x = 88

x = 88/4

x = 22

Therefore, the length x of the rectangle is 22

Answer 2

We can write this as an equation: [(x - 9) + (x - 9)] + (x + x) = 70

Steps to solve:

[(x - 9) + (x - 9)] + (x + x) = 70

Combine like terms:

(x + x + x + x) + (-9 - 9) = 70

Simplify.

4x - 18 = 70

Add 18 to both sides.

4x - 18 + 18 = 70 + 18

Simplify.

4x = 88

Divide 4 to both sides.

4x/4 = 88/4

Simplify.

x = 22

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Option D is the correct answer.

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Best Regards,

Wolfyy :)