Question

The length of a rectangle is 2 inches more than its width. The perimeter of the rectangle is 24 inches. The equation 2x + 2(x + 2) = 24, where x is the width in inches, represents this situation.

The value of x from the set {1, 3, 5, 7} that holds true for the equation is ___ . So, the width of the rectangle is ___ inches and its length is ___ inches

Answer 1

2x + 2(x + 2) = 24
2x + 2x + 4 = 24
4x = 24 - 4
4x = 20
x = 20/4
x = 5

The value of x that holds true for the equation is : x = 5.
So the width of the rectangle is 5 inches and the length is (x + 2 = 5 + 2) = 7 inches

Answer 2

The  value of x from the set {1, 3, 5, 7} that holds true for the equation is 5 . So, the width of the rectangle is 5 inches and its length is 7 inches

What is perimeter of rectangle?

The perimeter of a rectangle is defined as the sum of all the sides of a rectangle. For any polygon, the perimeter formulas are the total distance around its sides.

Formula of Perimeter of rectangle :

Perimeter of rectangle = 2(length + breath)

According to the question

Let width of rectangle = x

The length of a rectangle is 2 inches more than its width.

therefore,

length of rectangle = x+2

The perimeter of the rectangle is 24 inches.  

Now,

By using the formula of Perimeter of rectangle :

Perimeter of rectangle = 2(length + breath)

$24 = 2 (x + x + 2)$

$12 = 2x + 2$

$10 = 2x \\x = 5$

Therefore ,

width of rectangle = x = 5 inches

length of rectangle = x+2 = 7 inches

Hence, the  value of x from the set {1, 3, 5, 7} that holds true for the equation is 5 . So, the width of the rectangle is 5 inches and its length is 7 inches

To know more about perimeter of a rectangle  here:

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