In the floor plan for a house, one bedroom was
square with a square closet attached. The sides
of the bedroom were 8 times as large as the
sides of the closet, and the sum of the areas of
the two was 585 square feet. How long were the
sides of the bedroom and the closet?

Question

UpStudy AI · Accepted Answer

Let's solve the problem step by step.

1. **Define Variables:**
   - Let $$ x $$ be the length of one side of the **closet**.
   - Since the bedroom is square and its sides are 8 times as large as the closet, the length of one side of the **bedroom** is $$ 8x $$.

2. **Calculate Areas:**
   - **Area of the closet:** $$ x^2 $$
   - **Area of the bedroom:** $$ (8x)^2 = 64x^2 $$

3. **Set Up the Equation:**
   - The sum of the areas is given as 585 square feet:
     $$
     x^2 + 64x^2 = 585
     $$
     $$
     65x^2 = 585
     $$

4. **Solve for $$ x $$:**
   $$
   x^2 = \frac{585}{65} = 9
   $$
   $$
   x = \sqrt{9} = 3 \text{ feet}
   $$

5. **Find the Bedroom's Side Length:**
   $$
   8x = 8 \times 3 = 24 \text{ feet}
   $$

**Conclusion:**
- **Closet:** Each side is **3 feet** long.
- **Bedroom:** Each side is **24 feet** long.

**Answer:**  
Each closet side was 3 feet and each bedroom side was 24 feet long.
Each closet side was 3 feet and each bedroom side was 24 feet long.

In the floor plan for a house, one bedroom was
square with a square closet attached. The sides
of the bedroom were 8 times as large as the
sides of the closet, and the sum of the areas of
the two was 585 square feet. How long were the
sides of the bedroom and the closet?

Upstudy AI Solution

Answer

Solution

The Deep Dive

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In the floor plan for a house, one bedroom was square with a square closet attached. The sides of the bedroom were 8 times as large as the sides of the closet, and the sum of the areas of the two was 585 square feet. How long were the sides of the bedroom and the closet?

Upstudy AI Solution

Answer

Solution

The Deep Dive

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Latest Algebra Questions

In the floor plan for a house, one bedroom was
square with a square closet attached. The sides
of the bedroom were 8 times as large as the
sides of the closet, and the sum of the areas of
the two was 585 square feet. How long were the
sides of the bedroom and the closet?