Introduction

Given integers b and a, find the smallest integer h, such that there exists a triangle of height h, base b, having an area of at least a.

Example Input Output

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# Input:
2 2
# Output:
2

{: file="Input and Output” }

Explanation:
The task is to find the height of the triangle having base b = 2 and area a = 2. It turns out that the height is h = 2.

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# Input:
17 100
# Output:
12

{: file="Input and Output” }

Explanation:
The task is to find the height of the triangle having base b = 17 and area a = 100. It turns out that the height is h = 12 and the triangle has an area of 102.

Process

The area of a triangle is given by the formula:

$$
A = \frac{1}{2}bh
$$

where b is the base and h is the height of the triangle. Manupulating the formula, we get:

$$
h = \frac{2A}{b}
$$

I knew I needed to use the ceiling function to get the smallest integer h that satisfies the condition. So I used the ceil() function from the math.h library to round the calculated value of the height up to the next integer. The formula can be changed to:

$$
h = \lceil\frac{2A}{b} \rceil
$$

We are able to use this formula to calculate the height of the triangle given the base and area.

Code

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int lowestTriangle(int trianglebase, int area) {
    double height = ceil(2 * (double)area / (double)trianglebase);
    return (int)height;
}

{: file="Minimum Height Triangle.c” }

Afterthoughts

Upon applying the manipulated formula, I was able to return the minimum height of the triangle, given the base and the area.

However, All challenges come with their hurdles and I was met with some when I did this.

1. I initially used int for the height, but using a calculator to check the results, some results return a decimal value and int will truncate the decimal value. So, I changed the type to double and used ceil() to round up the value.
2. I needed to typecast the area and trianglebase to double to avoid integer division as the result of the division will be an integer.
3. The return value of the function is an int, so I had to typecast the height to int.

This solution passed all testcases.