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Hello,
Making an equation would be a good method to solve this problem.
The area of a rectangle is equal to
, where l is the length and w is the width of the rectangle.
If the area of the wall is 280280, we know = 280280
We also know that the length is 88 feet longer than twice the width. Twice the width is equal to
, and the length is 88 feet longer than that, so 
.
So, we have a system of equations:
Using the first equation, we can find the value of l and we get
We then plug in this value of l into the second equation, and we have:
Now, we can multiply by w on both sides, and subtract 280280 on both sides, and use the quadratic formula to get w ≈ 353, -397
The width of a wall cannot be negative, so the answer is 353 feet.
To find l, and make sure of our answers, we should check it with the original problem to make sure it checks out.
Doing this, we get:
Divide by 353 on both sides to get:
Now, we should check it with the equation
794 = 2(353) + 88
794 = 794, checks out.
So, the width of the wall of the barn is 353 feet, and the length of the wall of the barn is 794 feet.
Hope this helps! Feel free to contact me with any questions you may have.
Making an equation would be a good method to solve this problem.
The area of a rectangle is equal to
If the area of the wall is 280280, we know
We also know that the length is 88 feet longer than twice the width. Twice the width is equal to
So, we have a system of equations:
Using the first equation, we can find the value of l and we get
We then plug in this value of l into the second equation, and we have:
Now, we can multiply by w on both sides, and subtract 280280 on both sides, and use the quadratic formula to get w ≈ 353, -397
The width of a wall cannot be negative, so the answer is 353 feet.
To find l, and make sure of our answers, we should check it with the original problem to make sure it checks out.
Doing this, we get:
Divide by 353 on both sides to get:
Now, we should check it with the equation
794 = 2(353) + 88
794 = 794, checks out.
So, the width of the wall of the barn is 353 feet, and the length of the wall of the barn is 794 feet.
Hope this helps! Feel free to contact me with any questions you may have.
Answer:
a) CD = 41 m
b) 77.32°
c) 1380 square metres
Step-by-step explanation:
We can divide the trapezium as shown in the diagram below.
a) To find CD, we use Pythagoras Rule:
b) To find <BCD, we use trigonometric function SOHCAHTOA:
sin(BCD) = opp / hyp
sin(BCD) = 40 / 41
sin(BCD) = 0.9756
=> <BCD = 77.32°
c) The area of a trapezium is given as:
A = 1/2 (a + b) * h
where h = height = 40 m
a = top length = 30 m
b = bottom length = 39 m
A = 1/2 * (30 + 39) * 40
A = 1/2 * 69 * 40
A = 1380 square metres
