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 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?
160 square centimeters
150 square centimeters
600 square centimeters
300 square centimeters

Explanation:

Step1: Write the joint - variation formula

The area \(A\) of a triangle varies jointly with the height \(h\) and base \(b\), so \(A = kbh\), where \(k\) is the constant of variation.
Given \(A = 200\) when \(h = 25\) and \(b = 16\). Substitute into the formula: \(200=k\times16\times25\).

Step2: Solve for \(k\)

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Step3: Find the area for new \(h\) and \(b\)

Now, \(h = 20\) and \(b = 15\), and \(k=\frac{1}{2}\). Substitute into \(A = kbh\):

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Answer:

150 square centimeters