Question

The perimeter of a rectangle is 85 feet.The length of the rectangle is 2(x+16) andthe width is 3x - 1. What is the length of therectangle?A- 45.75 feetB- 36.6 feetC- 55 feetD- 23.3 feet

Answer 1

The perimeter of a rectangle is 85 feet. Therefore the perimeter is expressed as;

`\begin{gathered} P=2(L+W) \\ P=2(2\lbrack x+16\rbrack+\lbrack3x-1\rbrack) \\ P=2(2x+32+3x-1) \\ P=4x+64+6x-2 \\ \text{Where the perimeter is 85, you now have} \\ 85=4x+6x+64-2 \\ \text{Collect like terms, and you have} \\ 85-64+2=4x+6x \\ 23=10x \\ \text{Divide both sides by 10} \\ 2.3=x \\ \text{The length of the triangle is therefore;} \\ L=2(x+16) \\ L=2(2.3+16) \\ L=2(18.3) \\ L=36.6ft \end{gathered}`

The correct option is B; 36.6 feet