Question

A right triangle has sides of length n, n + 1, and n + 2. Monica uses the basic formula, area =1/2 base * height, to compute The area of the triangle and comes up with an area of n^2 + 3n +2 / 2. Sunil uses The same formula and comes up with an area of n^2 + n / 2. which area is correct? Explain.

Answer 1

Monica is incorrect and Sunil is correct.

Explanation:

In the right triangle the longest side is the hypotenuse.

If a right triangle has sides of length n, n + 1, and n + 2, then

• 1st leg = n;
• 2nd leg = n+1;
• hypotenuse = n+2.

Use the formula

`A=(1)/(2)\cdot \text{1st leg}\cdot \text{2nd leg}`

to find the area of the triangle.

So,

`A=(1)/(2)\cdot n\cdot (n+1)=(n^2+n)/(2)\ un^2.`

Thus, Monica is incorrect and Sunil is correct.