500=140+40h
minus 140 both sides
360=40h
divide y 40
9=h
9 hours
Hi! I'm happy to help!
To solve this, we first need to look at the perimeter equation:
P=2L+2W
We don't know our length, so we can represent it with x. Since our width is 2 feet shorter than x, we can represent it with x-2. Now, we plug these values into our equation:
56=2x+(2(x-2))
Let's simplify what the width is by multiplying:
56=2x+2x-4
Now, let's combine our 2xs
56=4x-4
Now, we just need to solve for x in order to find our length and width.
First, we need to isolate x on one side of the equation. We can do this by adding 4 to both sides:
56=4x-4
+4 +4
60=4x
Now, all we have to do is divide both sides by 4 and x will be fully isolated:
60=4x
÷4 ÷4
15=x
Now that we know x, let's plug this into our previous equations:
L=x=15
<u>L=15</u>
W=x-2=15-2=13
<u>W=13</u>
To verify our answers, we can plug this into our perimeter equation:
56=2(15)+2(13)
56=30+36
56=56
After double checking our answers, we know that our length is 15 and our width is 13.
I hope this was helpful, keep learning! :D
This problem is about adding up the surface area of all of the surfaces he will paint and then dividing it by 200 to find how many gallons he will need to buy. Since he won't paint his roof, we need to find the surface area of every square foot that he will paint. So to do this it is just doing the area formula A=L*W for rectangles, and A=1/2*H*W, for the triangles. So he will paint 2 triangular spaces, the front and the back, plus he will paint 4 rectangular walls. So let's do the very front section first. When looking straight at the front u see a rectangle and a triangle. So let's find the area of both. The rectangle we need to plug in the length, or in other words the height, which is 8 feet. The width is 12 ft. So what is 8 times 12? It is 96 sq. ft. So 96 square feet is the front rectangle. There is another rectangle on the back of the shed that's the same dimensions that he will paint, so instead of doing that again we can just multiply 96 sq ft by 2, which is 192 sq ft. Now let's do the 2 triangles he will paint. Both of the triangles are the same exact dimensions, so what we do is plug the numbers in, the height is 4 ft. So it looks like 1/2 * 4 ft * 12 ft. 1/2 of 4 is 2, so multiply 2 by 12, which equals 24. So one of the triangles has 24 sq ft, but since there is another one on the back side that he will paint, we multiply that by 2 to save time. This will equal 48 sq ft. Now all we have to do is the other two walls on the sides. This is the same formula, A= L*W. so length is the same as the other 2 rectangles because they are the same height, so the length is 8 ft. And the width is 20 ft. What is 20 times 8? 20 times 8 is 160 sq ft. Since there is another wall just like that on the other side, we multiply that by 2 to get 320 sq ft. Now we add all of it up. 320+ 48+ 192= 560 sq ft. So he will paint 560 sq ft. What is 560 divided by 200? It will be 2.8, so he will have to buy 2.8 gallons of paint. Since you can't buy 2.8 gallons of paint, he will really buy 3 gallons, so he will have some left over. Since 1 gallon cost $48, we will need to multiply 48 by 3, to give us 144. So he will spend $144 on paint to paint his shed. I hope this helps
