Repost:
Sarah has a rectangular corral for her horses. She wants to put new rail fencing all around the corral. What total lenght of fencing will she need.
Description of the corral: in my book it is square and around the square is a length of 28m and inside the square if you go diagonaaly its a lenght of 42m .
I tried and tried I don't get this question please help
http://www.jiskha.com/display.cgi?id=1244694224
If it's a square and the perimeter totals 28 m, just multiply 28 by $15 to get the cost before taxes.
If it's a square and EACH SIDE is 28 m, then multiply 28 x 4 x $15.
(If I'm wrong, a math teacher will correct me!)
My problem is more with the diagonal being 42. Using a^2 + b^2 = c^2, the sides would not be 28 if the diagonal was 42.
I'll explain it. There is a square in my book. Outside of the squar one of the sides is 28m. Inside the square going across from one corner to the other is 42m
To find the total length of fencing Sarah would need, we need to calculate the perimeter of the corral.
From the description you provided, it seems like the corral is a square with side length 28m and there is an inner square with a diagonal length of 42m.
To find the perimeter of the corral, we need to find the length of all four sides of the outer square. Since the corral is square, all sides have the same length, which is 28m. So, the perimeter of the outer square is 4 times 28m, which is 112m.
Now, let's understand the relationship between the outer square and the inner square. The diagonal of the inner square is equal to the length of the side of the outer square plus twice the width of the rail fencing.
Let's assume the width of the rail fencing is 'w' meters. So, based on the given information, we can write the equation:
42m = 28m + 2w
Now, we can solve this equation to find the width of the rail fencing.
Subtracting 28m from both sides, we get:
14m = 2w
Dividing both sides by 2, we get:
7m = w
So, the width of the rail fencing is 7 meters.
To find the total length of the rail fencing needed, we need to add the perimeter of the inner square to the perimeter of the outer square, and then subtract the length of the diagonal of the inner square, since the rail fencing only goes around the perimeter of the corral.
The perimeter of the inner square is 4 times the side length, which is 4 times 28m, which is 112m.
So, the total length of fencing Sarah will need is:
Perimeter of outer square + Perimeter of inner square - Length of diagonal of inner square
= 112m + 112m - 42m
= 224m - 42m
= 182m
Therefore, Sarah will need a total length of 182 meters of rail fencing for her rectangular corral.