Question

A gopher has dug holes in opposite corners of a rectangular yard. One length of the yard is

Answer 1

Answer:

20 yards

Step-by-step explanation:

21 + x = perimeter (x being the width because it is unknown)

so far this would look like an incomplete triangle, or in other words, it is connected to Pythagoras theorem.

a^2 +b^2 = c^2 but since we don't know one of the sides of the triangle, (a^2 in this case) we can reverse the equation to get our answer.

=

c^2 - b^2 = a^2

c would represent the 2 holes the gophers dig on opposite sides of the rectangular yard, and since we already know the length, we can use this equation.

c = 29

b = 21

a = x (unknown)

=

29^2 - 21^2 = x^2

now we can just square c (29) and b  (21)

29^2 = 841

21^2 = 441

so now the equation looks like

841 - 441 = x^2

now just some simple subtraction

841 - 441 = 400

so...

400 = x^2

and then to get x without the ^2 we can just get the square root of 400, which counters the ^2.

=

√400 = 20

so there you have it!

20 = x

or

20 = a

or

20 = the width!

there is probably a better way to do this, but I just like geometry lol.

Mark brainliest if this helped, and have a good day! :D