give the demensions of rectangles with the perimeters of 70 feet and length-to-width ratios of 3 to 4, 4 to 5, and 1 to 1.
Ok, the perimeter is 70 and perimeter = 2(length + width)
The ratio is length:with=3:4 so length = (3/4)width
70 = 2(length + width) =2((3/4)width +
width)
So 35 = (7/4)width
Can you finish it off?
If the ratio is 4:5 then 35=((4/5)width + width)
If it's 1:1 then 35 = 2*length = 2*width
Can you finish it off now?
I'm sorry I havn't done this in 20 years my son is in 7th grade doing 8th grade work and I guess the teacher expects the student to know this stuff. He has given no direction to the kids. Thank you for all your help. I will have to get a teaching book on Algebra so I can teach my child.
Ok. This is introductory algebra so you should have no trouble finding sources to help. If you look at the Jump box above you'll find lessons that cover this material on Jiskha.
Thank You, Thank you
You're welcome
Feel free to have your son post questions too. There are plenty of people helping here.
Let the width-to-length ratio be r. I am calling "length" the longest side, so r is less than or equal to 1.
Let a be the longest side length. The shortest side length is then a*r.
The perimeter is
70 = 2a (1 + r)
35 = a (1+r)
a = 35/(1+r)
Solve for a, using r values of 3/4, 4/5 and 1
When r = 3/4, a = 35/(7/4) = 20
The short side will then be 3/4 of 20, or 15. You do the others
To find the dimensions of a rectangle with a perimeter of 70 feet and a length-to-width ratio of 3 to 4, you can use the formula for perimeter:
Perimeter = 2(length + width)
Substituting the given values:
70 = 2(length + width)
Since the length-to-width ratio is given as 3 to 4, we can express the length in terms of the width by saying:
length = (3/4)width
Substituting this expression into the perimeter formula:
70 = 2((3/4)width + width)
Simplifying:
70 = 2((7/4)width)
35 = (7/4)width
To find the width, you can solve this equation for width by dividing both sides by (7/4):
width = 35 / (7/4) = 20
Now, substitute this value back into the expression for length:
length = (3/4) * 20 = 15
So, the dimensions of the rectangle with a length-to-width ratio of 3 to 4 and a perimeter of 70 feet are 15 feet by 20 feet.
Similarly, you can find the dimensions for the other given ratios:
For a length-to-width ratio of 4 to 5:
35 = (4/5)width + width
35 = (9/5)width
width = 35 / (9/5) = 17.78 (approx.)
length = (4/5) * 17.78 = 14.22 (approx.)
So, the dimensions are approximately 14.22 feet by 17.78 feet.
For a length-to-width ratio of 1 to 1:
35 = 2 * length = 2 * width
width = 35 / 2 = 17.5
length = width = 17.5
So, the dimensions are 17.5 feet by 17.5 feet.