the area of a triangle is 27. its height is 3 times the base. find the height and the base of the triangle.
a = 1/2 bh
h = 3b
a = 1/2 b*3b = 3/2 b^2
27 = 3/2 b^2
18 = b^2
b = 3√2
h = 9√2
check: a = 1/2 (3√2)(9√2) = 1/2 (27)(2) = 27
To find the height and base of a triangle, you can use the formula for the area of a triangle.
The formula for the area of a triangle is:
Area = (1/2) * base * height
Given that the area of the triangle is 27 and the height is 3 times the base, we can express this information mathematically as:
27 = (1/2) * base * (3 * base)
Let's solve for the base first. Multiply both sides of the equation by 2 to get rid of the fraction:
27 * 2 = base * (3 * base)
54 = 3 * base^2
Now divide both sides of the equation by 3 to isolate the base:
54 / 3 = base^2
18 = base^2
To find the value of the base, take the square root of both sides:
√18 = √(base^2)
Now, simplify the square root of 18:
√18 = base
Using a calculator, you'll find that the square root of 18 is approximately 4.24.
So, the base of the triangle is approximately 4.24.
To find the height, multiply the base by 3 (as given):
Height = 3 * 4.24
Height ≈ 12.73
Therefore, the height of the triangle is approximately 12.73 and the base is approximately 4.24.