A 2 feet tall child casts a shadow that is 3 feet long. Find the height of the boy whose shadow is `7(1)/(2)` feet long.

Answer

To solve the problem of finding the height of the boy whose shadow is 7.5 feet long, we can use the concept of proportion. Here’s a step-by-step solution:

### Step 1: Set up the proportion
We know that the height of the child is 2 feet and the length of the shadow is 3 feet. We want to find the height of the boy (let's call it \( x \)) whose shadow is 7.5 feet long. We can set up the proportion as follows:

\[ \frac{\text{Height of child}}{\text{Shadow of child}} = \frac{\text{Height of boy}}{\text{Shadow of boy}} \]

This translates to:

\[ \frac{2}{3} = \frac{x}{7.5} \]

### Step 2: Convert 7.5 to a fraction
To make calculations easier, we can convert 7.5 feet into a fraction.

\[ 7.5 = \frac{15}{2} \]

Now, our proportion looks like this:

\[ \frac{2}{3} = \frac{x}{\frac{15}{2}} \]

### Step 3: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:

\[ 2 \cdot \frac{15}{2} = 3 \cdot x \]

This simplifies to:

\[ 15 = 3x \]

### Step 4: Solve for \( x \)
Now, we can solve for \( x \) by dividing both sides by 3:

\[ x = \frac{15}{3} \]

Calculating this gives:

\[ x = 5 \]

### Conclusion
The height of the boy whose shadow is 7.5 feet long is **5 feet**.

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