Question

solve.
the faraj family is building a deck in their backyard with the dimensions 25ft by 15ft. there will be a bed of flowers surrounding the entire deck with a width of x feet. find the total area of the deck and flowers.

Explanation:

Step1: Determine the new length and width

The deck has dimensions 25 ft by 15 ft. The flower bed has a width of \( x \) feet on all sides, so the new length of the deck and flowers combined will be \( 25 + 2x \) (adding \( x \) feet to both the left and right sides) and the new width will be \( 15 + 2x \) (adding \( x \) feet to both the top and bottom sides).

Step2: Calculate the area

The area of a rectangle is given by the formula \( A = \text{length} \times \text{width} \). Substituting the new length and width, we get the area \( A=(25 + 2x)(15 + 2x) \).
Expanding this using the distributive property (FOIL method):
\[

$$\begin{align*} (25 + 2x)(15 + 2x)&=25\times15+25\times2x+2x\times15 + 2x\times2x\\ &= 375+50x + 30x+4x^{2}\\ &=4x^{2}+80x + 375 \end{align*}$$

\]

Answer:

The total area of the deck and flowers is \( 4x^{2}+80x + 375 \) square feet.