the length of a rectangular field is 18 m longer than the width. the field is enclosed with fencing and divided into two parts with a fence parallel to the shoter sides. if 216 m of fencing are required to the shoter sides. if 216 m of fencing are required, what are the dimensions of the outside rectangle?
shorter side --- x
longer side --- x+18
wouldn't we just get
2(x+18) + 3x = 216 ???
I get short side = 36
long side = 54
1944
To find the dimensions of the outside rectangle, we need to follow these steps:
1. Let's assume the width of the rectangular field is "x" meters.
2. According to the given information, the length of the field is 18 meters longer than the width. So the length would be "x + 18" meters.
3. The rectangular field is divided into two equal parts by a fence parallel to the shorter sides. Therefore, there are two shorter sides in total.
4. We are given that 216 meters of fencing are required for the shorter sides.
5. Since there are 2 shorter sides, each shorter side would require half of that, which is 216/2 = 108 meters of fencing.
6. The perimeter of a rectangle is given by the formula P = 2(length + width).
7. We know that the perimeter of the rectangle is 2(length + width) = 216 meters.
8. Plugging in the given values, we have: 2(x + 18 + x) = 216.
9. Simplifying the equation, we get: 2(2x + 18) = 216.
10. Expanding the equation, we have: 4x + 36 = 216.
11. Subtracting 36 from both sides, we get: 4x = 180.
12. Dividing both sides by 4, we have: x = 45.
13. So the width of the rectangular field is 45 meters.
14. Plugging this value back into the equation for the length, we have: x + 18 = 45 + 18 = 63.
15. Therefore, the length of the rectangular field is 63 meters.
16. Finally, the dimensions of the outside rectangle are: width = 45 meters and length = 63 meters.