The length of a rectangle is 4 inches more than its width, and its perimeter is 34 inches. What is the length and width of the rectangle?

Question

Violet Aldrich · Accepted Answer

Length #l = 10.5”#, Width #w = 6.5”#

Perimeter #P= 2l + 2w#

Given #l =( w + 4)”, P = 34”#

#:. 34 = 2(w+4) + 2w#

#4w + 8 = 34#

#w = 26/4 = 6.5”#

#l = w + 4 = 6.5 + 4 = 10.5”#

Noah Atkinson · Answer

length is #10.5# inches

width is #6.5# inches

Let length be #l# Let width be #w# Let perimeter be #P# First, we must construct an equation for these variables: #l=w+4# #P=34# But, Perimeter of a rectangle #=l+w+l+w# #=2l+2w# So: #34=2l+2w# But, since #l=w+4#, we can substitute for #l#, having only the #w# variable: #34=2(w+4)+2w# #34=2w+8+2w# #34=4w+8# Solve for #w#: #4w=34-8# #4w=26# #w=26/4# #w=6.5# inches Now, we can substitute #6.5# for #w# in the Perimeter Equation: #34=2l+2w# becomes: #34=2l+2*6.5# #34=2l+13# Solve for #l#: #2l=34-13# #2l=21# #l=21/2# #l=10.5# inches Thus, length is #10.5# inches Thus, width is #6.5# inches

Parker Allen · Answer

undefined Let $ w $ represent the width of the rectangle. Then the length of the rectangle is $ w + 4 $. The formula for the perimeter of a rectangle is $ P = 2(w + l) $, where $ P $ is the perimeter, $ w $ is the width, and $ l $ is the length. Substitute the given values into the formula and solve for $ w $. Once $ w $ is found, calculate the length $ l = w + 4 $. Finally, plug in the values for $ w $ and $ l $ to confirm they satisfy the condition that the perimeter is 34 inches.