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To solve for the missing length \( y \) in the given triangle, we need to use the formula for the area of a triangle:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

In this problem:
- The base is \( 14 \) inches.
- The area is \( 52.5 \) square inches.
- The height is represented by \( y \).

Substitute the known values into the formula:

\[
52.5 = \frac{1}{2} \times 14 \times y
\]

Now, solve for \( y \):

1. Multiply both sides by 2 to eliminate the fraction:

\[
105 = 14 \times y
\]

2. Divide both sides by 14:

\[
y = \frac{105}{14} = 7.5 \, \text{inches}
\]

So, the missing length \( y \) is **7.5 inches**.

Would you like further details on this solution or have any questions?

Here are 5 related questions to explore:
1. How do you find the area of a triangle if the base and height are known?
2. What would happen to the height if the area of the triangle were doubled?
3. How can you determine the height of a triangle if you only know the area and the base?
4. Why is the area formula for a triangle \(\frac{1}{2} \times \text{base} \times \text{height}\)?
5. How do you find the area of a triangle if given all three sides?

**Tip:** Remember that in right triangles, the height is always perpendicular to the base, which simplifies calculations like these.

What is the missing length y if the base of the triangle is 14 inches and the area is 52.5 square inches?

Learn how to calculate the missing height of a triangle with a base of 14 inches and an area of 52.5 square inches. This problem uses basic geometry and algebra concepts, making it perfect for students in Grades 6-8.

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