JAMB 2010 Mathematics · Question 21

If two smaller sides of a right angled triangle are 4cm and 5cm, find its area

Options

A.10 cm2
B.6 cm2
C.24 cm2
D.8 cm2

Answer: A. 10 cm2

Explanation written with AI and checked against the answer key

Analyze the question: The "two smaller sides" of a right-angled triangle are the two shorter sides, which are the legs (the sides that meet at the right angle). The hypotenuse is always the longest side. So the base is 4 cm and the height is 5 cm. Concept: Area of a triangle = ½ × base × height. In a right-angled triangle, the two legs serve as the base and height. Solution: Area = ½ × 4 × 5 Area = ½ × 20 Area = 10 cm² Check: The hypotenuse would be √(4² + 5²) = √41 ≈ 6.4 cm, which is longer than both 4 and 5. This confirms that 4 and 5 are the two smaller sides. Answer: Option A, 10 cm². Tip: In right-angled triangle questions, if you are given the two legs, just use ½ × product of the legs. You don't need the hypotenuse for the area. Watch out for questions that give the hypotenuse and one leg, because then you must find the other leg with Pythagoras first.

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