A triangular traffic island has a base half as long as its height. The island has an area of 100 m2 . Find the base and the height.
h * h/2 * 1/2 = 100
h = 20
To find the base and height of the triangular traffic island, we can use the formula for the area of a triangle:
Area = (1/2) × base × height
Given that the area is 100 m² and the base is half as long as the height, we can set up the following equations:
100 = (1/2) × base × height ... Equation 1
base = (1/2) × height ... Equation 2
Substitute Equation 2 into Equation 1 to solve for height:
100 = (1/2) × (1/2) × height × height
Divide both sides by (1/4):
100 × 4 = height × height
400 = height²
Take the square root of both sides to solve for height:
√400 = height
height = 20 m
Substitute the value of height back into Equation 2 to find the base:
base = (1/2) × 20
base = 10 m
Therefore, the height of the triangular traffic island is 20 m and the base is 10 m.