Question

If the area of the rectangle shown is 150 square feet, we can use the equation 23 - 5x = 150 to find its dimensions. If the solution to the equation is x = 10, what are the dimensions of the rectangle?

A) 2 ft x 75 ft
B) 5 ft x 30 ft
C) 10 ft x 15 ft
D) 15 ft x 20 ft
E) 25 ft x 6 ft

Answer 1

By solving the given area equation for x and determining that x = 10, we can deduce that the dimensions of the rectangle are 10 ft x 15 ft (Option C), as these dimensions multiplied together give the area of 150 square feet.

Step-by-step explanation:

To find the dimensions of the rectangle using the given equation 23 - 5x = 150, we first need to solve the equation for x. If x is determined to be 10, we then substitute the value back into the dimensions of the rectangle.

Let's solve the equation step by step:

Subtract 23 from both sides: 23 - 5x - 23 = 150 - 23

This simplifies to: -5x = 127

Now, divide both sides by -5: x = 127 / -5

So, x = 10 (since we were already given x = 10 as the solution).

Once we have x, we need to understand how it fits into the dimensions of the rectangle. Given that the area of the rectangle is equal to the product of its length and width (l × w), and we have an area of 150 square feet, we need to find two numbers that when multiplied together give us 150.

Remembering that the solution for x is 10, we can assume that one of the dimensions includes this number, so the correct dimensions of the rectangle would be 10 ft x 15 ft (Option C), as 10 × 15 equals the area of 150 square feet.