Page 32 - Math Course 3 (Book 2)

Properties of Squares and Rhombi

Diagonals of a Square
Your Turn!

Example Diagonals of a Square

Kayla has a square garden whose length and width
CONSTRUCTION are each 25 feet. If she places a fountain exactly in

A square table has four legs that are 2 feet apart. the center of the garden, how far is the center of the
The table is placed over an umbrella stand so that fountain from one of the corners of the garden?
the hole in the center of the table lines up with the B C
hole in the stand. How far away from a leg is the
center of the hole?

B C
E 25 ft

E 2 ft
A 25 ft D

A. 25 feet
A 2 ft D B. 12.5 feet
C. 17.7 feet
Let ABCD be the square formed by the legs of D. 15 feet
the table. Since a square is a parallelogram, the
diagonals bisect each other. Since the umbrella Answer
stand is placed so that its hole lines up with the
hole in the table, the center of the umbrella pole is
at point E, the point where the diagonals intersect.
Use the Pythagorean Theorem to find the length of
a diagonal.

AC² = AD² + CD²
AC² = 2² + 2²

AC² = 8
AC ≈ 2√2 or 2.83 feet
The distance from the center of the pole to a leg is
equal to the length of AE.

1
AE = AC
2
1
≈ (2.83)
2
≈ 1.42

The center of the pole is about
Answer
1.4 feet from a leg of a table.

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