Jillian Fluet’s POTW solution

A B

CD

E

F

G

H

Draw a square and label the line segments so AP=7 BP=35 CP=49 and DP=x. Then drop altitudes from point P to each side of the square. Label the point on AB, E, the point on BC, F, the point on CD, G, and the point on DA, H.

P

EP, AH, BF have a length of a

GP, DH, CF have a length of s-a

EP, BE, CG have a length of b

HP, AE, DG have a length of s-b

1

2

3

4

Then use the Pythagorean Theorem to solve for x.

Triangle 1: a²+b² =(35)²

Triangle 2: (s-a)²+b² =49²

Triangle 3: a²+(s-b)² =7²

Triangle 4: (s-a)²+(s-b)² =x²

Add the 2nd and 3rd triangles together and subtract the sum of the 1st and 4th triangles.

Then you get: 0= 49²+7²-35²-x²

Solve:0= 49²+7²-35²-x²

x² =49²+7²-35²

x² =35²

x=35 or x= ( 35)

x=35 because you can’t have a negative length