Question

1. the area of a rectangular pool is 10 more than three times its width. choose the correct set - up to represent an equation for the area of this garden.

a. (a = 10w+3)
b. (a = 3w + 10)
c. (a = 10w-3)
d. (a = 3w - 10)

1. the area of a rectangular garden is 12 less than 4 times its perimeter. choose the correct set - up to represent an equation for the area of the pool.

a. (a = 12-4p)
b. (a = 12p - 4)
c. (a = 4p-12)
d. (a = 4 - 12p)

1. the length of a rectangle is 10 inches more than twice a number. write the equation for the length of the rectangle.
2. the width is 5 inches less than a number. write the equation for the width of the rectangle.
3. the length of a rectangle is 8 inches less than three times a number. write the equation for the length of the rectangle.
4. the width is 4 inches more than half of a number. write the equation for the width of the rectangle.
5. the length of a square is (4x + 5). the width of the square is (2x+15). if the length and width are the same, find the value of (x). what is the side - length of the square?

(x=)
side length =

Explanation:

Step1: Set up equation for square side - lengths

Since length and width of a square are equal, we set up the equation $4x + 5=2x + 15$.

Step2: Solve for $x$

Subtract $2x$ from both sides: $4x-2x + 5=2x-2x + 15$, which simplifies to $2x+5 = 15$. Then subtract 5 from both sides: $2x+5 - 5=15 - 5$, getting $2x=10$. Divide both sides by 2: $\frac{2x}{2}=\frac{10}{2}$, so $x = 5$.

Step3: Find side - length of the square

Substitute $x = 5$ into either the length or width expression. Using the length expression $4x + 5$, we have $4\times5+5=20 + 5=25$.

Answer:

$x = 5$
Side Length $=25$