Question

2) The shape of a playground is a parallelogram. The city is going to treat the asphalt with sealant this spring with cans that will cover 4 square yards each. The figure below is a drawing of the playground, For how many cans of sealant does the city need to budget for the treatment, if the playground has a perimeter of 34 yards and the height is 1.4 yards less than the diagonal side of the parallelogram? 10.6 yd 6.4 yd a. Write the equation in words. b. Find the unknown height. c. Calculate the area of playground. d. Choose a variable for the unknown quantity and write the equation with the substituted values. e. Solve the equation. Include appropriate units in your answer. f. How many cans of sealant are needed?

Answer 1

In this situation, you have a parallelogram with lateral sides of L length and top and bottom sides of length D. The letter h represents the height of the parallelogram.

L=6.4 yd and D=10.6 yd. The perimeter is the sum of all 4 edges, so perimeter=2*L+2*D

a) If one can cover 4 square yards and you need to find how many cans you will need for the whole playground area, then you need to find the total area which is calculated by its height times its base (D), so it would be h*D=area. This area divided by 4 square yards will give you the number of cans you need.

b) If the height is 1.4 yards less than the diagonal side, then

`h=L-1.4=6.4-1.4=5\text{ yards}`

c)Then the area is given by:

`h\cdot D=5\cdot10.6=53\text{ square yards}`

d)The number of cans can be represented by a variable called n (n as in number), so:

`n=(area)/(4)=(53)/(4)`

e) Then, by calculating:

`(53)/(4)=13.25\text{ cans}`

f) You will need 14 cans of sealant, you will only use some of it from the last can