a triangle has a base 3cm greater than 5x its height. what is the area of the triangle when its length is 6cm
Let's use the following variables:
- Base of the triangle: b
- Height of the triangle: h
According to the problem:
The base of the triangle is 3cm greater than 5 times its height, so we can express this relationship as:
b = 5h + 3
To find the area of the triangle, we use the formula: Area = (1/2) * base * height
Given that the length (base) of the triangle is 6cm, we substitute this value into the equation as:
6 = 5h + 3
Subtracting 3 on both sides:
6 - 3 = 5h
3 = 5h
Dividing both sides by 5:
3/5 = h
h = 0.6 cm
Now that we have the height of the triangle, we can substitute this value into the equation for the base:
b = 5h + 3
b = 5(0.6) + 3
b = 3 + 3
b = 6 cm
Finally, to find the area of the triangle:
Area = (1/2) * base * height
Area = (1/2) * 6 * 0.6
Area = 1.8 square centimeters
Therefore, the area of the triangle is 1.8 square centimeters.