Solve the following: 1) find the length of a lane 5m wide can be covered by 50,000 bricks of size 22 cm by 15 cm?

1 Answer
smendyka
Mar 21, 2018

See a solution process below:

Explanation:

First, convert the dimensions of the bricks to meters. The conversion factor for centimeters to meters is:

#1" cm" = 0.01" m"#

Therefore: 22cm is:

#22 xx 1" cm" = 22 xx 0.01" m"#

#22" cm" = 0.22" m"#

And: 15cm is:

#15 xx 1" cm" = 15 xx 0.01" m"#

#15" cm" = 0.15" m"#

Next, we can find the area of 1 brick. The formula for the area of a rectangle is:

#A = l xx w#

Substituting the length and width of a brick gives:

#A = 0.22" m" xx 0.152" m" = 0.033"m"^2#

We can now find the area of the lane by multiplying the area of 1 brick by the 50,000 bricks used to cover the lane.

#50000 xx 0.033"m"^2 = 1650"m"^2#

We now have the area of the lane and the width of the lane from the problem so we can substitute this into the area formula to find the length of the lane:

#1650"m"^2 = l xx 5"m"#

#(1650"m"^2)/color(red)(5"m") = (l xx 5"m")/color(red)(5"m")#

#(1650"m"^color(red)cancel(color(black)(2)))/color(red)(5color(black)(cancel(color(red)("m")))) = (l xx color(red)(cancel(color(black)(5"m"))))/cancel(color(red)(5"m"))#

#(1650"m")/color(red)(5) = l#

#330"m" = l#

#l = 330"m"#

The lane is 330 meters long

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