Question

A rectanglular building lot has the dimensions shown. If its area is 2,700 ft2, what is the value of x? (Do not include units when you type in your answer.)

Answer 1

The value of x is 70, as determined by solving the quadratic equation representing the area of a rectangular building lot with dimensions x + 20 and x - 40, given an area of 2,700 ft².

To find the area of the rectangular building lot, you can use the formula:

`\[ \text{Area} = \text{Length} * \text{Breadth} \]`

Given that the length is x + 20 feet and the breadth is x - 40 feet, you can substitute these values into the formula:

`\[ 2700 = (x + 20) * (x - 40) \]`

Now, you can solve this quadratic equation for x. Expand and simplify the equation:

`\[ 2700 = x^2 - 40x + 20x - 800 \]`

Combine like terms:

`\[ 2700 = x^2 - 20x - 800 \]`

Move all terms to one side of the equation:

`\[ x^2 - 20x - 800 - 2700 = 0 \]`

Combine constant terms:

x^2 - 20x - 3500 = 0

Now, factor the quadratic equation or use the quadratic formula to find the values of x. Factoring, you get:

(x - 70)(x + 50) = 0

This equation has two solutions: x - 70 = 0 or x + 50 = 0.

If x - 70 = 0, then x = 70.

If x + 50 = 0, then x = -50.

Since dimensions cannot be negative, the only valid solution is x = 70. Therefore, the value of x is 70.