The base of a triangle is four times its height. If the area of the triangle is 242 square millimeters, find its base and height.
area= 1/2 b*h
242=1/2 4h*h=2h^2
h^2=121
h=11
b=4h=44
Sure, let me calculate that for you. 🤡
Let's call the height of the triangle h. According to the problem, the base (b) of the triangle is four times its height, so we can express it as b = 4h.
The formula to calculate the area of a triangle is 1/2 * base * height. Since we already know the area, we can plug in the given values and solve for h:
242 = 1/2 * (4h) * h
Simplifying the equation:
242 = 2h^2
Dividing both sides by 2:
121 = h^2
Taking the square root of both sides:
h = √121
Therefore, the height of the triangle is h = 11 mm.
Now, let's substitute this value of h back into the equation for the base:
b = 4h
b = 4 * 11
b = 44 mm
So, the base of the triangle is 44 mm and the height is 11 mm.
Hope these numbers don't make your head spin. 🤡
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 of the triangle is 242 square millimeters, we can set up the equation:
242 = (1/2) * Base * Height
Next, we are given that the base of the triangle is four times its height. We can represent this relationship as:
Base = 4 * Height
Now we can substitute the value of Base from the second equation into the first equation:
242 = (1/2) * (4 * Height) * Height
Now, let's simplify the equation:
242 = 2 * Height^2
Divide both sides of the equation by 2:
121 = Height^2
Take the square root of both sides of the equation:
Height = √121
Height = 11
Now that we have the height, we can substitute it back into the second equation to find the value of the base:
Base = 4 * Height
Base = 4 * 11
Base = 44
Therefore, the height of the triangle is 11 millimeters and the base of the triangle is 44 millimeters.