To find the base and height of the triangle, we can use the formula for the area of a triangle:
Area = (1/2) × base × height
Given that the area is 80 in², we can set up the equation:
80 = (1/2) × base × height
Now, let’s denote the base as 5x and the height as 2x since the ratio of the base to height is 5:2.
Substituting these values into our area equation gives us:
80 = (1/2) × (5x) × (2x)
This simplifies to:
80 = 5x²
Now we can solve for x²:
x² = 80/5
x² = 16
This means x = 4.
Now we can find the base and height:
Base = 5x = 5 × 4 = 20 in
Height = 2x = 2 × 4 = 8 in
So, the base of the triangle is 20 inches and the height is 8 inches.