SOLUTION: Concrete blocks of length (14/25)m were laid end to end along the four sides of a rectangular lawn 28 m long and 21 m wide. (a) How many blocks were required to complete one laye

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Question 1210646: Concrete blocks of length (14/25)m were laid end to end along the four sides of a rectangular lawn 28 m long and 21 m wide.
(a) How many blocks were required to complete one layer?
(b) If each block costs GH¢1.80 and the cost of labour is one-third the cost of a block, find the total cost of laying the blocks
Answer by KMST(5398) About Me  (Show Source):
You can put this solution on YOUR website!
WHAT THE TEACHER PROBABLY EXPECTS:
(a) How many blocks were required to complete one layer?
Calculate the perimeter like the teacher showed in class.
If the teacher expects you to write a formula, such as Perimeter=2%28length%2Bwidth%29 , write the formula the teacher provided.
Otherwise, Perimeter=28m%2B21m%2B28m%2B21m=98m will probably do.
Then divide that length by the length of a block to find the number of blocks:
98%2F%2214+%2F+25%22=98%2A%2825%2F14%29=highlight%28175%29

b) If each block costs GH¢1.80 and the cost of labour is one-third the cost of a block, find the total cost of laying the blocks.
The cost of the blocks, in GH¢, is 1.80%2A175=315
THe cost of the labour is 315%2F3=105 .
Total cost, in GH¢, is 315%2B105=highlight%28420%29

THE REAL-LIFE PROBLEM:
In real life, things are not so simple, and we do not know many details of how exactly to do this job.
There are many questions.
(a) the number of blocks were required to complete one layer:
With all lengths in m, the ratio of lengths is the number of blocks required to fill one length:
28%2F%2814%2F25%29=28%2A25%2F14=2%2A25=highlight%2850%29
Is that what was called "one layer"?
with 2%2A50blocks=100blocks we get a line of blocks 28 m long along each long edge.
Getting a line of blocks along one 21-m width with blocks would be the ratio of lengths:
21%2F%2814%2F25%29=21%2A25%2F14=%2821%2F14%29%2A25=%283%2F2%29%2A25=75%2F2=37.5 ,
so the number of blocks required to line the 2 widths would be
2%2A%2875%2F2%29=75
However, the devil is in the details.
How exactly are we lining that rectangular lawn, and how wide are those blocks?
Are they placed just along the outside, like this:
%22%3F%22
My drawing show how it would look in a photo taken with a drone.
Lining all 4 sides as shown in the design will require
100blocks%2B75blocks=highlight%28175blocks%29
Lining the inside edges would take less blocks because the rectangles in my drawing would be inside the lawn and would overlap at the corners.
If we put the blocks outside as in my drawing, do we have to fill completely or partially those empty corners?
Are those blocks sold by the block or in packages of 100?
Should we buy more blocks to fill corners, or because blocks could break accidentally, or when trying to cut them in half?
What is the width of those blocks? It would matter if we have to fill those corners in my drawing.
The width of the blocks in my drawing is 1/2 m, and their height is not visible,
because we are looking from high above.