Question

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.
Left side (5.5) in
Right side (7.7) in
Bottom of triangle (x)


Question 1 options:

5.4 in


12.2 in


11 in


9.5 in

Answer 1

To find the missing side \( x \) of the triangle with the given left side (5.5 in) and right side (7.7 in), we can use the Pythagorean theorem, which applies to right triangles. According to the theorem:

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

where \( c \) is the length of the hypotenuse and \( a \) and \( b \) are the lengths of the other two sides. In this case, we need to determine whether \( x \) is the hypotenuse or one of the other sides. Since the problem does not specify which side is the hypotenuse, we will assume \( x \) is the longest side (the hypotenuse).

1. Assign the sides:
- \( a = 5.5 \)
- \( b = 7.7 \)
- \( c = x \)

2. Apply Pythagorean theorem:
\[
5.5^2 + 7.7^2 = x^2
\]

3. Calculate \( 5.5^2 \) and \( 7.7^2 \):
\[
5.5^2 = 30.25
\]
\[
7.7^2 = 59.29
\]

4. Sum the squares:
\[
30.25 + 59.29 = 89.54
\]
\[
x^2 = 89.54
\]

5. Take the square root to find \( x \):
\[
x = \sqrt{89.54} \approx 9.5
\]

Thus, the length of the missing side \( x \) is approximately 9.5 inches.

The correct answer, rounded to the nearest tenth, is:

**9.5 in**