9. A rectangle has a width that is 2 feet longer than four times the length. What is the length of the rectangleif the perimeter is 64 feet? (HINT: Draw a picture and use algebra to solve)
Accepted Solution
A:
Answer:6 feetStep-by-step explanation:Perimeter = 2L + 2WSince you know the perimeter is 64 feet, you would plug that into the perimeter side. 64 = 2L + 2WYou also know the width is 2 feet longer than 4 times the length.64 = 2L + 2(2 + 4L) ----> Multiply 2 * 2 and 2 * 4l64 = 2L + 4 + 8L ----> Subtract 4 from each side-4 -460 = 2L + 8l ----> add these two60 = 10L/10 /10 -----> divide by 10 on each side6 = LNow that we know the length, find the width.64 = 2(6) + 2(2 + 4(6)) -----> multiply 2 * 6 and 4 * 664 = 12 + 2(2 + 24) -------> add 24 and 264 = 12 + 2(26) -------> multiply 2 and 26Before you go any further, you now know that the width is 26 feet. Continue solving.64 = 12 + 5264 = 64Everything checks out.The length is 6 feet and the width is 26 feet.