Question

Lars put stakes in his backyard, as shown in the diagram below, to separate sections of his garden.



Lars stretched 24 yards of a string from stake X to stake Y and 18 yards of the string from stake Y to stake Z. The two strings meet at a right angle.

He wants to stretch the string from stake Z to stake X next. What is the distance from stake Z to stake X?
A.
30 yards
B.
450 yards
C.
42 yards

Answer 1

To find the distance from stake Z to stake X, we can use the Pythagorean theorem. The distance from stake X to stake Y is 24 yards, and the distance from stake Y to stake Z is 18 yards. Since the strings meet at a right angle, the distances form a right triangle.

The sides of this triangle are:
- One side (XY) = 24 yards
- The other side (YZ) = 18 yards
- The hypotenuse (ZX) is what we need to find.

According to the Pythagorean theorem:

\[
c^2 = a^2 + b^2
\]

where \( c \) is the hypotenuse (ZX), and \( a \) and \( b \) are the other two sides (XY and YZ).

Substituting in our values:

\[
ZX^2 = XY^2 + YZ^2
\]
\[
ZX^2 = 24^2 + 18^2
\]
\[
ZX^2 = 576 + 324
\]
\[
ZX^2 = 900
\]

Now, take the square root to find ZX:

\[
ZX = \sqrt{900} = 30 \text{ yards}
\]

So, the distance from stake Z to stake X is **30 yards**.

The correct answer is **A. 30 yards**.