A rectangular dog run has a width of 2 root 7 yards and a length of 10 root 7 yards.

Question

here is the rest of the problem:

The owner has 2 dogs that need to be separated so she is going to put a diagonal fence connected on each corner. a. What would the length and width be in decimals? Round to one decimal place. b. How long is the diagonal fence? Write your answer in radical and decimal form. c. The old fence doesn’t match the new fence so she wants to replace it. How many yards of fencing does she need? Write your answer in radical and decimal form.

Answer 1

To find the length and width in decimal form, use your calculator to multiply 2 times root 7 and 10 times root 7:

2 * √7 = 5.3

10 * √7 = 26.5

If the owner puts a diagonal fence up in her yard, she has just created two right triangles of identical dimensions. This means we can use the Pythagorean theorem (a²+b²=c²) to find the length of the diagonal. The diagonal of a right triangle is always the c while the legs are the a and b:

a²+b²=c²

(2√7)²+(10√7)²=c²

4*7 + 100 * 7 = c²

28 + 700 = c²

√728 = √c²

c = 2√182 decimal form = 27.0 yards

I'm assuming the old fencing needing replaced is the length and width and not the diagonal. So we just need to find the perimeter of the old fence using 2w + 2l:

2w + 2l

2(2√7 ) + 2(10√7) = 4√7 + 20√7 = 24√7 decimal form = 24*√7 = 63.5 yards

If you have questions please don't hesitate to leave me a comment!