The length of a rectangle is 5 yd less than double the width, and the area of the rectangle is 52 yd^2 . How do you find the dimensions of the rectangle?

Question

Eli Assouline · Accepted Answer

Width = 6.5 yds, length = 8 yds.

Define the variables first. We could use two different variables, but we have been told how the length and width are related. Let the width be #x" width is the smaller side"# The length = #2x -5# "Area = l x w" and the area is given to be 52 squ yards. #A = x(2x-5) = 52# #2x^2 -5x = 52" quadratic equation"# #2x^2 -5x -52 = 0# To factorise, find factors of 2 and 52 which cross-multiply and subtract to give 5. #color(white)(xxx)(2)" "(52)# #color(white)(xx.x) 2" 13 "rArr 1xx13 = 13# #color(white)(xx.x) 1" 4 "rArr2xx4 = 8" "13-8 = 5# We have the correct factors, now fill in the signs. We need -5. #color(white)(xxx)(2)" "(-52)# #color(white)(xx.x) 2" - 13 "rArr 1xx-13 = -13# #color(white)(xx.x) 1" +4 "rArr2xx+4 = +8" "-13+8 = -5# #(2x-13)(x+4) = 0# Each factor could be equal to 0 #x = 6.5 or x = -4 # (reject) The width = 6.5 yards. Now find the length: 6.5 x 2 -5 = 8 yards Check: Width = 6.5yds, length = 8yds Area = 6.5 x 8 = 52

Hazel Anglin · Answer

Length#= 8 yd#
Width #= 6.5 yd#.

Let width be #=x# Therefore, length #=2x -5# We know that #"Area" = "Length" xx "Width"# Inserting given and assumed numbers we get #52=(2x-5)xx x# rearranging we obtain #2x^2 -5x -52 = 0# To factorize we use split the middle term method. We have two parts of middle term as #-13x and 8x#. The equation becomes #2x^2-13x+8x-52 = 0# Paring and taking out common factors we have #x(2x-13)+4(2x-13) = 0# #=>(2x-13)(x+4) = 0# Setting each factor equal to #0#, we have two roots #(2x-13)=0and (x+4) = 0# #x = 13/2=6.5# # x = -4 #, rejected as width can not be a #-ve# value #:.#Width #= 6.5 yd#. And length#= 2xx6.5 -5 = 8 yd# Check: Area #= 8xx 6.5 = 52yd^2#

Kennedy Adams · Answer

undefined To find the dimensions of the rectangle, you can follow these steps:

1. Let the width of the rectangle be represented by "w" yards.
2. Since the length is 5 yards less than double the width, the length can be represented as "2w - 5" yards.
3. The area of a rectangle is calculated by multiplying its length by its width. So, the equation for the area of the rectangle is: Area = length × width.
4. Substitute the expressions for length and width into the area equation and solve for "w."
5. Once you find the value of "w," use it to find the length of the rectangle.
6. Check your solution by verifying that the area of the rectangle is indeed 52 square yards.