A carpenter cuts a wooden support bracket in the shape of a right-angled triangle, shown in the diagram, with the two shorter sides measured in centimetres....
Question 1 Report
A carpenter cuts a wooden support bracket in the shape of a right-angled triangle, shown in the diagram, with the two shorter sides measured in centimetres.
- Find the length of the side marked \(x\), the longest edge of the bracket. Give your answer in the form \(a\sqrt{b}\). (3)
- Write down the perimeter of the bracket in the form \(p + q\sqrt{r}\). (1)
Answer Details
Since the bracket is right-angled, Pythagoras' theorem applies: the square of the longest side (the hypotenuse) equals the sum of the squares of the two shorter sides.
- (a) [3]. \(x^2 = 6^2 + 4^2 = 36+16 = 52\), so \(x = \sqrt{52}\). Since \(52 = 4\times13\) and \(4\) is a perfect square, \(x=\sqrt{4\times13}=2\sqrt{13}\) cm. Marks are for the correct use of Pythagoras, the value 52, and simplifying the surd to \(2\sqrt{13}\).
- (b) [1]. The perimeter is the sum of all three sides: \(6+4+2\sqrt{13} = 10+2\sqrt{13}\) cm.
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