Question 334845: if the square box is 20 feet from corner to corner what would be the dimensions of the square in sq yds Found 2 solutions by CharlesG2, solver91311:Answer by CharlesG2(834) (Show Source):
You can put this solution on YOUR website! if the square box is 20 feet from corner to corner what would be the dimensions of the square in sq yds
20 feet is the diagonal (hypotenuse) measurement of the square box
use Pythagorean Theorem
a^2 + b^2 = c^2, since square a = b, so 2a^2 = c^2, and c = 20 feet
2a^2 = 20^2 = 400
a^2 = 200 square feet, this is area of the square
a = 100 * 2 = 10sqrt(2) feet this is the length of a side of the square
1 yard = 3 feet
10sqrt(2) feet * 1/3 * yards/feet = (10/3)sqrt(2) yards per side of the square
The diagonal of a square creates two isosceles right triangles with the diagonal of the square as the hypotenuse. The three sides of an isosceles right triangle are in proportion:
Verification of this claim is left as an exercise for the student. (Hint: use Pythagoras with an isosceles triangle with hypotenuse of 1 and sides of )
Hence, if the diagonal of the square is 20, then the hypotenuse of the triangle is 20 and the side of the triangle must be .
The area of a square is the measure of the side of the square squared. So calculate:
John
My calculator said it, I believe it, that settles it
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