Question

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.
Left side (x)
right side (7.5) ft
Bottom of triangle (4.5) ft


Question 2 options:

4 ft


8.7 ft


6 ft


9.6 ft

Answer 1

To find the missing side \( x \) of the triangle, we can apply the Pythagorean theorem, which states that in a right triangle:

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

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

In your case:

- One side (bottom of the triangle) is \( 4.5 \) ft (let's call this \( a \)).
- The other side (right side) is \( 7.5 \) ft (let's assume this is the hypotenuse \( c \)).
- The missing side is \( x \) (let's call this \( b \)).

Using the Pythagorean theorem:

\[
(4.5)^2 + x^2 = (7.5)^2
\]

Calculating the squares:

\[
20.25 + x^2 = 56.25
\]

Now, we isolate \( x^2 \):

\[
x^2 = 56.25 - 20.25
\]
\[
x^2 = 36
\]

Taking the square root of both sides:

\[
x = \sqrt{36} = 6
\]

So, the length of the missing side \( x \) is \( 6 \) ft.

Among the options provided, the answer would be:

**6 ft**