The area of a triangle varies jointly with the height of the triangle and the length of its base. The area of one triangle is 200 square centimeters when its height is 25 centimeters and its base length is 16 centimeters. What is the area of a triangle having a height of 20 centimeters and a base length of 15 centimeters?
a = kbh
a/bh is constant, so you want a such that
a/(20*15) = 200/(25*16)
Beautiful J
To find the area of a triangle with a height of 20 centimeters and a base length of 15 centimeters, we need to use the concept of joint variation.
Step 1: Write the equation for joint variation.
The equation for joint variation is given as:
Area = k * height * base
where "Area" represents the area of the triangle, "height" represents the height of the triangle, "base" represents the length of the base of the triangle, and "k" is the constant of variation.
Step 2: Find the constant of variation.
We can find the constant of variation (k) by substituting the given values of the area, height, and base into the equation:
200 = k * 25 * 16
Simplifying this equation further:
k = 200 / (25 * 16)
k = 200 / 400
k = 0.5
Step 3: Use the constant of variation to find the area.
Now, we can use the constant of variation (k) to find the area of a triangle with a height of 20 centimeters and a base length of 15 centimeters:
Area = 0.5 * 20 * 15
Area = 150 square centimeters
Therefore, the area of a triangle with a height of 20 centimeters and a base length of 15 centimeters is 150 square centimeters.
To solve this problem, we need to use the concept of joint variation between the area of a triangle, the height, and the length of its base. Joint variation implies that the area varies directly with both the height and the base length.
Let's denote the area of a triangle as A, the height as h, and the base length as b.
Given that the area of one triangle is 200 square centimeters when its height is 25 centimeters, and its base length is 16 centimeters, we can write the joint variation equation as:
A = k * h * b,
where k is a constant.
Plugging in the given values, we get:
200 = k * 25 * 16.
Now, we can solve for k:
k = 200 / (25 * 16),
k = 0.5.
With the value of k, we can now find the area of a triangle with a height of 20 centimeters and a base length of 15 centimeters:
A = 0.5 * 20 * 15,
A = 150 square centimeters.
Therefore, the area of a triangle having a height of 20 centimeters and a base length of 15 centimeters is 150 square centimeters.