A contractor is building a fenced-in area at a daycare. The area will be rectangular with the length of its base equal to half the length of the height. The total area will be 5000 square feet. Determine the length of fencing the contractor will use

Accepted Solution

Answer:The length of fencing will be [tex]300\ ft[/tex]Step-by-step explanation:Step 1Find the dimensions of the rectanglewe know thatThe area of a rectangle is equal to[tex]A=bh[/tex]In this problem we have[tex]A=5,000\ ft^{2}[/tex]so[tex]5,000=bh[/tex] -----> equation A[tex]b=\frac{h}{2}[/tex] -----> equation BSubstitute equation B in equation A[tex]5,000=(\frac{h}{2})h[/tex] [tex]10,000=h^{2}[/tex]square root both sides[tex]h=100\ ft[/tex]Find the value of b[tex]b=\frac{h}{2}[/tex] -----> [tex]b=\frac{100}{2}=50\ ft[/tex]step 2Find the length of fencingThe perimeter of a rectangle is equal to[tex]P=2(b+h)[/tex] we have[tex]h=100\ ft[/tex][tex]b=50\ ft[/tex]substitute[tex]P=2(50+100)=300\ ft[/tex]