Question

a rectangular garden has a length of $(4x + 5)$ inches and a width of $(3x - 1)$ inches. find the length and width of the garden if the perimeter is 36 feet.
enter the correct values in the boxes.
show hints
the length is $square$ feet, and the width is $square$ feet.

Explanation:

Step1: Convert perimeter to inches

Since 1 foot = 12 inches, $36 \times 12 = 432$ inches

Step2: Recall rectangle perimeter formula

Perimeter $P = 2(\text{length} + \text{width})$
Substitute values: $432 = 2[(4x+5)+(3x-1)]$

Step3: Simplify the equation

First simplify inside the brackets: $(4x+5)+(3x-1)=7x+4$
Equation becomes: $432 = 2(7x+4)$
Divide both sides by 2: $216 = 7x+4$

Step4: Solve for x

Subtract 4 from both sides: $216-4=7x$
$212=7x$
$x=\frac{212}{7}=30.2857$

Step5: Calculate length in inches

Length $=4x+5=4\times30.2857+5=121.1428+5=126.1428$ inches
Convert to feet: $\frac{126.1428}{12}=10.5119\approx10.5$ feet

Step6: Calculate width in inches

Width $=3x-1=3\times30.2857-1=90.8571-1=89.8571$ inches
Convert to feet: $\frac{89.8571}{12}=7.4881\approx7.5$ feet

Answer:

The length is 10.5 feet, and the width is 7.5 feet.