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Pythagorean theorem

Pythagorean theorem

Problem Statement

In this problem, we will use  Pythagorean theorem to    calculate the diagonal of various  sized frames. The equation for     Pythagorean theorem is  a² + b²    = c ². By squaring 'a' and 'b', 'c'    can be calculated then square     rooted to find 'x'

How long are the diagonals of a 9" x 12" rectangular picture frame?

x

x

9"

12"

To find the diagonal of a 9" x 12" frame, you first have to input the formula for Pythagorean theorem which is:

After you have the formula, substitute the numbers provided for the letters:

Then calculate and convert:

Which you then square-root to find X:

81 + 144 = 225²

9²+ 12² = X²

a²+ b²= c²

225 = 15

X = 15²

X

9"

12"

what are the measurements of the leg on a 20" x 32.8" frame

To find the measurements of the leg on a 20" x 32.8" frame you have to start with the Pythagorean theorem:

Because we are finding the leg of the triangle instead of the diagonal, the 'X' is placed in the 'b' spot.

Next, you substitute the numbers in the problem in exchange for the letters:

Then you calculate and convert:

400 + X² = 1076

After, you subtract 400 from both sides:

(by subtracting 400 from 400 it becomes zero and cancels itself out)

1076- 400 = 676

Lastly, you square-root the final number and that is the number that X equals.

√676= 26

X = 26²

20² + X² = 32.8²

a² + b² = c²

32.8"

X

20"

what is the length of the diagonal side of a 10" x 37" frame

To find the length of the diagonal side of a 10" x  37" frame, you once again need to use Pythagorean theorem.

a² + b² = c²

Then you plug in the numbers provided, into the place where the letters were:

10² + 37² = c²

Next, you calculate and convert to find c²:

100 + 1369 = 1469

Lastly you square-root it to find X:

√(1469) = 38.3

X = 38.3²

x

10"

12"

By Hannah Micu and Lily Suehiro

the end.