Stephanie wants to paint a mural on a rectangular wall that has an area of 36 3/4square feet. If the width is 101/2feet long, what is the height of the wall on which Stephanie will paint the mural?

To find the height of the wall, we use the formula for the area of a rectangle:

\[
\text{Area} = \text{Height} \times \text{Width}
\]

Given:
- Area = \( 36 \frac{3}{4} \) square feet
- Width = \( 10 \frac{1}{2} \) feet

We need to solve for the height. First, let's convert the mixed numbers into improper fractions:

1. Convert \( 36 \frac{3}{4} \):
\[
36 \frac{3}{4} = \frac{36 \times 4 + 3}{4} = \frac{144 + 3}{4} = \frac{147}{4}
\]

2. Convert \( 10 \frac{1}{2} \):
\[
10 \frac{1}{2} = \frac{10 \times 2 + 1}{2} = \frac{20 + 1}{2} = \frac{21}{2}
\]

Now, using the formula for area:

\[
\frac{147}{4} = \text{Height} \times \frac{21}{2}
\]

Solve for the height by dividing both sides by \( \frac{21}{2} \):

\[
\text{Height} = \frac{\frac{147}{4}}{\frac{21}{2}} = \frac{147}{4} \times \frac{2}{21}
\]

Simplify:

\[
\text{Height} = \frac{147 \times 2}{4 \times 21} = \frac{294}{84} = \frac{7}{2} = 3 \frac{1}{2} \, \text{feet}
\]

Thus, the height of the wall is \( 3 \frac{1}{2} \) feet.

Would you like further clarification, or do you have any questions?

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Here are some related questions:

1. How would you calculate the perimeter of the wall?
2. What if the area were doubled, how would the height change?
3. How do you find the diagonal length of the wall?
4. How would changing the width to 12 feet affect the height?
5. How can you represent the area of a rectangle with algebraic expressions?

**Tip:** When working with mixed numbers in geometry problems, always convert them to improper fractions for more straightforward calculations.

Stephanie wants to paint a mural on a rectangular wall that has an area of 36 3/4 square feet. If the width is 10 1/2 feet long, what is the height of the wall on which Stephanie will paint the mural?

Learn how to find the height of a rectangular wall with an area of 36 3/4 square feet and a width of 10 1/2 feet. This solution involves key geometric concepts such as calculating the area of a rectangle and working with improper fractions. Suitable for students in Grades 6-8.

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