A rectangular exercise mat has a perimeter of 36 feet. The length of the mat is twice the width. Write and solve an equation to determine the length in feet, Of the mat. Then find the area in square feet of the mat.
Accepted Solution
A:
Answer:Part a) The length of the mat is [tex]12\ ft[/tex] Part b) The area of the mat is [tex]72\ ft^{2}[/tex]Step-by-step explanation:step 1Find the lengthLetL-----> the length of the rectangleW---> the width of the rectanglewe know thatThe perimeter of rectangle is[tex]P=2(L+W)[/tex][tex]P=36\ ft[/tex]so[tex]36=2(L+W)[/tex][tex]18=(L+W)[/tex] ----> equation A[tex]L=2W[/tex] -----> equation Bsubstitute equation B in equation A[tex]18=(2W+W)[/tex]solve for W[tex]18=3W[/tex][tex]W=18/3=6\ ft[/tex]Find the value of L[tex]L=2(6)=12\ ft[/tex] step 2Find the areaThe area of rectangle is equal to[tex]A=LW[/tex]substitute the values[tex]A=(12)(6)=72\ ft^{2}[/tex]