Question

A architect wants to create a rectangular room in a house. She wants it to have a total area of 255 square feet, and it should be 10 feet longer than it is wide. What dimensions should she use for the room? Round to the nearest hundredth of a foot.

Answer 1

The answer to your question is length = 21.73 and width = 11.73

Explanation:

Data

Total area = 255 ft²

length = x + 10

width = x

Formula

Area of a rectangle = length x width

Substitution

255 = (x + 10)(x)

Expand

255 = x² + 10x

Equal to zero

x² + 10x - 255 = 0

Solve with the quadratic formula

`x = \frac{-10 +- \sqrt{10^(2) -4(1)(-255)}}{2(1)}`

x =
`(-10 +-√(100 + 1020))/(2)`

x =
`(-10 +- √(1120))/(2)`

x =
`(-10 +- 33.47)/(2)`

x₁ = 11.73 x₂ = -21.73

There are no negative dimensions so the answer is 11.73.

Length = 11.73 + 10 = 21.73 ft