The diagram shows a right-angled triangle with shorter sides of length 9 cm and 12 cm. (a) Calculate the length of the hypotenuse. [2] (b) Work out the peri...
Question 1 Report
The diagram shows a right-angled triangle with shorter sides of length 9 cm and 12 cm.
(a) Calculate the length of the hypotenuse. [2]
(b) Work out the perimeter of the triangle. [2]
(c) Work out the area of the triangle. [2]
Answer Details
(a) Adding the squares of the two shorter sides gives the hypotenuse: \(9^2 + 12^2 = 81 + 144 = 225\) [M1]. The square root gives \(\sqrt{225} = 15\) cm [A1].
(b) The perimeter is the sum of all three sides: \(9 + 12 + 15\) [M1], giving 36 cm [A1].
(c) The two shorter sides are perpendicular, so they serve as the base and height: area \(= \frac{1}{2} \times 9 \times 12\) [M1], giving \(54 \; \text{cm}^2\) [A1].
Exam tip: 9, 12, 15 is the 3, 4, 5 triple scaled by 3, letting every part of this question be solved without a calculator once the triple is recognised.
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