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WAEC 2019 Mathematics · Question 29

Make b the subject of the relation lb = 12\frac{1}{2} (a + b)h

Options

  1. A.ah2l−h\frac{ah}{2l - h}
  2. B.2l−hal\frac{2l - h}{al}
  3. C.al2l−h\frac{al}{2l - h}
  4. D.al2−h\frac{al}{2 - h}

Answer: A. ah2l−h\frac{ah}{2l - h}

Explanation written with AI and checked against the answer key

Analyze the question: We need to rearrange the relation so that b stands alone on one side. The relation is lb = ½(a + b)h. Concept: To make a variable the subject, collect every term containing that variable on one side, factorise it out, then divide. Solution: Start with: lb = ½(a + b)h Multiply both sides by 2 to remove the fraction: 2lb = (a + b)h Expand the bracket: 2lb = ah + bh Collect the b terms on the left: 2lb − bh = ah Factorise b: b(2l − h) = ah Divide both sides by (2l − h): b = ah / (2l − h) Check with numbers: Let a = 2, h = 2, l = 3. Then b = (2×2)/(6 − 2) = 4/4 = 1. Left side: lb = 3×1 = 3. Right side: ½(2 + 1)(2) = 3. ✓ Tip: In "change of subject" questions, when the subject appears on both sides, always gather those terms on one side and factorise. Then divide by the bracket. Substituting simple numbers is a fast way to verify your answer in the exam.

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