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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