Question

Please help me with this problem:2.The length of a rectangular floor is 4 feet longer than its width w. The area of the floor is 525 ft^2.(a)Write a quadratic equation in terms of w that represents the situation.(b)Solve the quadratic equation using one of the methods covered in Unit 4 and then clearly state what are the dimensions of the floor.Show your work.

Answer 1

(a)

`W^(2)+4W-525=0`

(b)

Width: 21 feet

Length: 25 feet

Explanation:

Given:

Width (W) = W ft

Length (L) = (4 + W) ft

Area (A) = 525 ft^2

(a)

The area of a rectangle is equal to the product of its length and width, therefore:

`\begin{gathered} A=L\cdot W \\ \\ \text{ We replacing} \\ \\ 525=(4+W)\cdot(W) \\ \\ 4W+W^2=525 \\ \\ W^2+4W-525=0 \end{gathered}`

(b)

We solve the equation by factoring:

`\begin{gathered} W^(2)+4W-525=0 \\ \\ 4W=-21W+25W \\ \\ W^2-21W+25W-525=0 \\ \\ W(W-21)+25(W-21)=0 \\ \\ (W-21)(W-25)=0 \\ \\ W-21=0\rightarrow W=21 \\ \\ W+25=0\rightarrow W=-25 \end{gathered}`

The width of the rectangle is equal to 21 feet and the length of the rectangle is equal to 25 feet.