Question

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 270 square centimeters when its height is 30 centimeters and its base length is 18 centimeters. what is the area of a triangle having a height of 25 centimeters and a base length of 16 centimeters?
○ 225 square centimeters
○ 400 square centimeters
○ 800 square centimeters
○ 200 square centimeters

Explanation:

Step1: Find the constant of variation

The area formula for a triangle is $A=\frac{1}{2}bh$. Since $A$ varies jointly with $b$ and $h$, we can write $A = kbh$. Given $A = 270$ square - centimeters, $b = 18$ centimeters and $h = 30$ centimeters. Substitute these values into the equation:
$270=k\times18\times30$
Solve for $k$:
$k=\frac{270}{18\times30}=\frac{270}{540}=\frac{1}{2}$

Step2: Calculate the area of the new triangle

Now we know $k = \frac{1}{2}$, $b = 16$ centimeters and $h = 25$ centimeters. Use the formula $A = kbh$.
$A=\frac{1}{2}\times16\times25$
$A = 200$ square centimeters

Answer:

200 square centimeters