WAEC 2011 Mathematics · Question 14

G varies directly as the square of H, If G is 4 when H is 3, find H when G = 100

Options

A.15
B.25
C.75
D.225

Answer: A. 15

Explanation written with AI and checked against the answer key

Analyze the question G varies directly as the square of H, so G = kH². We find k first, then use it to find H when G = 100. Concept Direct variation: G ∝ H² means G = kH², where k is a constant. Solution Step 1: Find k using G = 4 when H = 3. 4 = k(3²) 4 = 9k k = 4/9 Step 2: Use G = 100. 100 = (4/9)H² H² = 100 × 9/4 = 225 H = √225 = 15 (taking the positive value) Answer H = 15, which is option A. Check: G = (4/9)(15²) = (4/9)(225) = 100 ✓ Tip: Remember to take the square root at the end. Students often stop at H² = 225 and pick D (225), which is a common trap. Whenever the variation involves a square, the last step is always a square root.

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