SOLUTION: A building's length 10meters less than twice its width.the sidewalk around the building is 2meters wide and the area of the sidewalk alone is 216square meters.find the length of th
Algebra.Com
Question 968764: A building's length 10meters less than twice its width.the sidewalk around the building is 2meters wide and the area of the sidewalk alone is 216square meters.find the length of the building
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the area of the sidewalk is equal to the area of the building plus the sidewalk minus the area of the building.
the area of the sidewalk is given as 216.
A1 = area of the building.
A2 = area of the building plus the sidewalk.
A2 - A1 = 216.
L = length of the building
W = wisth of the building.
the sidewalk is 2 meters wide.
the length of the building plus the width of the sidewalk on both sides is equal to L + 4.
the width of the building plus the width of the sidewalk on both sides is equal to W + 4.
we have:
A1 = L * W
A2 = (L+4) * (W + 4)
we know that A2 - A1 is equal to 216 because that's the area of the sidewalk and the area of the sidewalk was given as 216 square meters.
area of the sidewalk byh itself is therefore equal to A2 - A1 which is equal to (L+4) * (W+4) - L*W.
Simplify this equation to get:
LW + 4W + 4L + 16 - LW = 216.
combine like terms to get 4W + 4L + 16 = 216
subtract 16 from both sides of the equation to get 4W + 4L = 200.
you are given that the length of the building is equal to 10 meters less than two times the width of the building.
the formula for that is L = 2W - 10.
in the equation of 4W + 4L = 216, replace L with 2W - 10 to get 4W + 4(2W-10) = 200
simplify to get 4W + 8W - 40 = 200
combine like terms to get 12W - 40 = 200
add 40 to both sides of the equation to get 12W = 240
divide both sides of the equation by 2 to get W = 20.
if W = 20, then L = 2W - 10 = 2(20) - 10 = 30.
you have W = 20 and L = 30.
that's your solution.
the diagram shown below shows what this looks like:
< img src = "http://theo.x10hosting.com/2015/050601.jpg" alt="$$$"
RELATED QUESTIONS
A sidewalk of uniform width surrounds a rectangular building. How wide is the sidewalk if (answered by scott8148)
A concrete sidewalk that goes around a football field is 4 yards wide. The length of the (answered by josgarithmetic)
a rectangular building is 25m long and 15m wide. a path of constant width is laid around... (answered by checkley77)
A rectangular building is 2 meters longer than twice the width. The area of ground floor... (answered by basketball1127)
The perimeter of a rectangular building is 1200 feet. The length of the building is 2... (answered by checkley77)
A rectangular garden is 5 ft longer than twice its width. It has a sidewalk 3 feet wide... (answered by ikleyn)
A rectangular parking lot has a width that is eight feet less than its length.... (answered by ankor@dixie-net.com)
The length of a garden is 5 feet longer than its width. A 2 foot wide sidewalk... (answered by mananth)
The length of a rectangular garden is 5 feet longer than its width. The garden is... (answered by mathanator)