Unit 5 – Rates, Ratios, and Proportions
Lesson 4 – Proportions and Scale
Black Handout
Black – Proportions and Scale
1. Meagan needs to find out how tall a tree is in her yard. She doesn’t know how tall she
is, but she knows her shadow is 10’ 7½” (this means 10 feet and 7½ inches). She also
knows that she is 5” shorter than Mark, and his shadow is 11’ 8”. If the tree’s shadow
is 110’, how tall is the tree? Remember that there are 12 inches in 1 foot.
Solutions
1. 44 feet
Meagan height: n
Meagan’s shadow: 127.5 inches
Mark: n + 5
Mark’s shadow: 140 inches
n (Meagan 's height )
n + 5 (Mark 's height )
=
127.5 (Meagan 's shadow ) 140 (Mark 's shadow )
Cross-multiply: 140n = 127.5n + 637.5
Get the n’s on one side of the equation: 12.5n = 637.5
N = 51
Meagan is 51 inches
51 inches (Meagan 's height )
n (Tree 's height )
=
127.5 inches (Meagan 's shadow ) 110 (Tree 's shadow )
Cross-multiply: 127.5n = 5610
Divide both sides by 127.5 : n = 44 feet.
1
Unit 5 – Rates, Ratios, and Proportions
Lesson 4 – Proportions and Scale
Black Handout
Bibliography Information
Teachers attempted to cite the sources for the problems included in this problem set. In some cases,
sources may not have been known.
Problems
Bibliography Information
1
Zaccaro, Edward. Challenge Math (Second
Edition): Hickory Grove Press, 2005.
2