Question

If the perimeter of a rectangular flower bed is 30 feet, and its area is 44 square feet, what is the length of each of its shorter sides ?

• A. $11$ feet
• B. $5$ feet
• C. $4$ feet
• D. $8$ feet

Answer 1

The correct option is C $4$ feet

4 feet: Set up equations to represent the area and perimeter of the flower bed:

$A=l\times w$ $p=2(l+w)$

Then, substitute the known values for the variables A and P:

$44=I\times w$ $30=2(1+w)$

Solve the two equations using the substitution method:

$l=\frac{44}{w}$

$30=2(\frac{44}{w}+w)$ Multiply the entire equation by $\frac{w}{2}$.

$15w=44+w^2$ Solving the quadratic equation yields two solutions:

$w^2-15w+44=0$ 4 and 11. Each represents a possible side length.

$(w-11)(w-4)=0$ Since you were asked to find the length of the

$w=4,11$ shorter side, the answer is the smaller of the two possible values, 4. (Option C)