Question

Jorge is building a rectangular pen for some goats. If he needs an area of 290 ft² and he has 78 ft of fence, what should the dimensions of the pen be?

Area of a rectangle =LW
Perimeter of a rectangle= 2L+2W
a) Length = 15 ft, Width = 19 ft
b) Length = 13 ft, Width = 17 ft
c) Length = 20 ft, Width = 14 ft
d) Length = 18 ft, Width = 15 ft

Answer 1

Jorge needs the dimensions of a rectangle with a perimeter of 78 ft and an area of 290 ft². None of the provided options meet both requirements. There might be a mistake in the problem or the options given.

Step-by-step explanation:

Jorge is building a rectangular pen for some goats and needs to find the dimension that will give him an area of 290 ft² with 78 ft of fencing available. To find this, we use the formulas for the area of a rectangle (LW = area) and the perimeter of a rectangle (2L + 2W = perimeter), where L is length and W is width.

Firstly, we need to remember that the perimeter (which is the total length of fence Jorge has) is equal to 78 ft, so:

2L + 2W = 78

We can simplify this equation by dividing everything by 2:

L + W = 39

Now, we need to consider the area requirement, which is:

LW = 290

To find the correct dimensions, we need to solve these two equations together numerically or graphically. None of the given dimensions (a) 15 ft x 19 ft, (b) 13 ft x 17 ft, (c) 20 ft x 14 ft, and (d) 18 ft x 15 ft satisfy both the perimeter and area requirements because for example (a) would result in a perimeter of 2(15) + 2(19) = 68 ft, which does not equal 78 ft, and an area of 15 * 19 = 285 ft², which is not 290 ft².

After checking all options this way, it turns out that none of them work, which suggests there might be a mistake in the problem or the provided options.