For algebra masters only..radical expression.. help?

Question

A soccer field is 20 yd wide and 30 yd long. Find the length of the diagonal of such a field. Give and exact answer as a radical expression and an approximation to three decimal places.

The exact length of the diagonal is ___ yards.(using radicals)



the length of the diagonal is ____ yards.
(round to nearest thousandth)

Answer 1

d² = 20² + 30²
d² = 400 + 900
d² = 1300
d = 13 x 100
d = 10.√13 yds ≈ 36.056 yds

Answer 2

Step 1: Draw a picture. This allows you to see that it's a triangle and that you can apply the Pythagorean Theorem.

Step 2: Let a = 20 and b = 30.

Step 3: Apply the Pythagorean Theorem. Recall: a^2 + b^2 = c^2. Therefore, 20^2 + 30^2 = c^2, so c = sqrt(1300) yards. This is your exact answer.

Step 4: Plug it into a calculator for the approximate answer. sqrt(1300) ~ 36.055 yards.

Answer 3

Use Phythagoras theorem.
Diagonal, d
Then
d^2 = 20^2 + 30^2 = 1300
So d = 10sqrt(13) yards

d = 36.055512754639892931192212674705
= 36.056 yards to nearest thousandth

Answer 4

Using phythagoras theorem.
d² = a² + b²

Let say a is wide and b is long and the solution goes like this:
d² = 20² + 30²
d = √(20² + 30²)
d = √1300
d = 36.056 yards

Answer 5

Use Pythagoream's theorem.

length^2 + width^2 = diagonal^2
(20yd)^2 + (30 yd)^2 = diagonal^2
400 + 900 = diagonal^2
1300 = diagonal ^2
diagonal = sqrt(1300)

sqrt(1300) = sqrt(100 * 13) = sqrt(100) * sqrt(13)
sqrt(1300) = 10sqrt(13) = 36.055 yd.