Question

If the area of the triangle with vertices (x, 3), (4, 4) and (3, 5) is 4 square units, find x.

Answer 1

Given: The vertices are (x, 3), (4, 4) and (3, 5) and the area is 4 square units.

Step-wise calculation:

1. Use the determinant formula:

Area = `1/2 | x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|`

2. Substitute (x₁, y₁) = (x, 3), (x₂, y₂) = (4, 4), (x₃, y₃) = (3, 5): 

2 × Area = |x(4 – 5) + 4(5 – 3) + 3(3 – 4)| 

= |–x + 8 – 3| 

= |–x + 5|

3. Since Area = 4 

2 × Area = 8

So, |–x + 5| = 8.

4. Solve: –x + 5 = 8 

⇒ x = –3 or –x + 5 = –8 

⇒ x = 13

⇒ x = –3 or x = 13