To solve the problem, consider that the wall can be divided into a rectangle and a right triangle. Given the dimensions and the properties of a [tex]\( 45^\circ-45^\circ-90^\circ \)[/tex] triangle, follow these steps:
1. Identify the Given Lengths and Properties:
- One leg of the [tex]\( 45^\circ-45^\circ-90^\circ \)[/tex] triangle is given as [tex]\( 6.5 \)[/tex] feet.
- In a [tex]\( 45^\circ-45^\circ-90^\circ \)[/tex] triangle, both legs (perpendicular sides) are equal.
- The hypotenuse of a [tex]\( 45^\circ-45^\circ-90^\circ \)[/tex] triangle is [tex]\( \text{leg} \times \sqrt{2} \)[/tex].
2. Calculate the Hypotenuse:
- Since the legs are given as [tex]\( 6.5 \)[/tex] feet, the hypotenuse can be calculated as:
[tex]\[
\text{Hypotenuse} = 6.5 \times \sqrt{2}
\][/tex]
- Plugging in the value, we get:
[tex]\[
\text{Hypotenuse} = 6.5 \times \sqrt{2} \approx 9.192
\][/tex]
3. Calculate the Height of the Wall:
- For the height [tex]\( h \)[/tex] of the trapezoid wall, consider the height to be the same as the length of the hypotenuse (if this is specifically stated as part of the trapezoid's dimensioning).
Therefore, the height [tex]\( h \)[/tex] of Maria's trapezoid wall is approximately:
[tex]\[
h = 9.192 \text{ feet}
\][/tex]
In conclusion, the value of [tex]\( h \)[/tex], the height of the wall, is approximately [tex]\( 9.192 \)[/tex] feet.
