I need help with my daughters homework. I know a little bit of algebra but it has been about 15 years since I have done it. She switched schools recently and there was a learning gap in the schools. The problem is: give the demensions of rectangles with the perimeters of 70 feet and length-to-width ratios of 4 to 5. I hoping this could be done step by step so I can work it out and show her how to do it. Any help would be appreciated.
Let length be l, and w for width.
2L + 2W= perimeter or = 70
2W= 70 - 2L
W= 35 - L
Now, one knows the L/W ratio, so
L/W=4/5 and manipulating that
L= 4W/5
{Putting that in the above equation)
W= 35 - L = 35 - 4W/5
adding 4W/5 to both sides..
W+ 4W/5 =35
9W/5= 35
9W=35*5
W= 35*5/9= 19.4 feet
but L+ W= 35, so L= 35-19.4 feet
Check: Is L/W= 4/5 ?
15.6/18.4= .8, so it checks
Thank you so much!
You're welcome! I'm glad I could help you with your daughter's homework. Here's a step-by-step explanation of how I solved the problem:
1. Let's assign variables to represent the dimensions of the rectangle. We'll use "L" for length and "W" for width.
2. The problem tells us that the perimeter of the rectangle is 70 feet. The formula for the perimeter of a rectangle is 2L + 2W.
3. So, we can write the equation 2L + 2W = 70.
4. Now, let's simplify the equation. We can start by isolating one variable. In this case, I chose to isolate "W".
2L + 2W = 70
2W = 70 - 2L
5. Next, we can solve for "W" by dividing both sides of the equation by 2.
W = (70 - 2L)/2
W = 35 - L
6. We also know that the length-to-width ratio is 4 to 5. This means that the length is 4 times the width. We can express this as the equation L = (4W)/5.
7. Now, we can substitute the expression for L into the equation for W.
W = 35 - L
W = 35 - (4W)/5
8. To simplify this equation, let's first get rid of the fraction by multiplying both sides by 5.
5W = 175 - 4W
9. Combining like terms, we get:
9W = 175
10. Divide both sides of the equation by 9 to solve for "W".
W = 175/9
W ≈ 19.4 feet
11. Now that we have the value for "W", we can substitute it back into the equation for L to find its value.
L = 35 - W
L = 35 - 19.4
L ≈ 15.6 feet
12. Finally, we can check if the length-to-width ratio is indeed 4 to 5 by dividing the calculated length by the calculated width.
L/W = 15.6/19.4 ≈ 0.8
The ratio L/W is approximately 0.8, which confirms that the dimensions of the rectangle satisfy the given length-to-width ratio of 4 to 5.
I hope this step-by-step explanation helps you understand the solution better. If you have any more questions, feel free to ask!