This is a booklet for our math using pythagorean theorem,

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Pythagorean Theorem

Susan and her picture frame problem

By: Samantha Zack, and Natalie Zendejas

9'' (a)

Problem solving - Pythagoras - Problem #2

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

STEP THREE: Find the square root of the answer

STEP TWO: Do the steps in the equation at the top. (square both of the given number and determine which missing letter to fill in

81(9 x 9) + 144(12 x 12) = 255( c    )

12'' (b)

2

c

225  = 15

2

STEP ONE: Figure out which part of the equation is missing. In this case side c (the long side) is missing.

Explanation-

Susan wants to find out how long the diagonals are of the picture frame. By asking for the diagonals we are automatically trying to find out the missing side of a triangle. The equation for figuring out how to solve the missing side of a triangle is:  a    +  b     =   c     (the equation above). So that is how we figure out weather or not to do Pythagorean theorem.

a    +     b       =   c

2

2

2

2

2

2

6'' (a)

QUESTION TWO: Susan has another picture she want to put in a frame; the picture she has is 6''  x   12''.  How long are the diagonals?

STEP ONE: Figure out which part of the equation is missing. In this case side c (the long side) is missing.

STEP TWO: Do the steps in the equation at the top. (square both of the given number and determine which missing letter to fill in

STEP THREE: Find the square root of the answer

c

9'' (b)

The steps for this equations are pretty much the same as the last problem.

Explanation-

Once again Susan has another picture in need of a frame. Like last time we know the measurements of sides a and b, and c is the side we are trying to solve for. As it says above one first needs to square both of the given numbers, then one will add those to numbers and square root the answer.

36  +   81  =  117 ( c   )

a   +   b    =  c

6    +    9       =     c

2

2

117   =  10.8''

2

10.8''

2

2

2

2

b

STEP TWO: This is where it gets different from the first two. One has to subtract 144 from 289 but in order to make the equation balanced you has to subtract 144 from each side (subtract 144 from 144 and 289).

STEP THREE: After step two you are left with the equation b   = 145. Once we have this all we have to do is square root the number and that is how you get what b equals.

QUESTION THREE: Susan found one more picture. She knows that one of the sides is 12'' and the diagonals are 17''. How long is the missing side

b    =  145

145    = 12.04''

2

b =  12.04''

-

144  +  b    =  289

144                144

____

0

12'' (a)

17'' (c)

b    =

2

2

-

145

____

2

Explanation-

Once again Susan has a picture frame problem except only this time she does not know what one of the sides it. In order to find the length of the side she has to subtract 144 from both sides of the equation. Then once she does she square roots the answer to find out how long side b is.

This question is slightly different than the other two

STEP ONE: This idea is the same as the last two questions. You have to find the missing side and how that plugs into the equation. In this case now the side that is missing is side b.

144   +  b    =  289

12   +   b     =    17

2

2

2

2