Stage 9 - Q1 - 2 marks
Find the hypotenuse \(x\). All lengths are in cm.
Hint
Identify the side opposite the right angle before choosing the formula.
Stage 9 - Q2 - 2 marks
Find \(x\) to 1 decimal place. Lengths are in cm.
Hint
The final length is a root, not the sum of the squares.
Stage 9 - Q3 - 3 marks
Find \(x\) to 2 decimal places. Lengths are in metres.
Hint
Keep all intermediate digits.
Stage 9 - Q4 - 3 marks
A learner adds 14 and 48 to find the hypotenuse. Correct the method and result. Lengths are in cm.
Hint
Pythagoras relates the squares of the sides.
Stage 9 - Q5 - 4 marks
A rectangular panel is 13 cm by 18 cm. Find its diagonal to 1 d.p.
Hint
Use two perpendicular sides of the rectangle.
Stage 9 - Q6 - 4 marks
A rectangular panel is 15 cm by 20 cm. Find its diagonal to 1 d.p.
Hint
Use two perpendicular sides of the rectangle.
Stage 9 - Q7 - 5 marks
A right triangle has legs 9 and 40. Enlarge both by factor 5. Find the new hypotenuse and explain its scale factor.
Hint
Factor the scale factor squared out of the sum.
Stage 9 - Q8 - 5 marks
Rectangles have sides 15 by 18 and 14 by 19. They have equal perimeters. Which diagonal is longer? Compare exactly.
Hint
Avoid rounding the two roots; compare their radicands.
Stage 9 - Q9 - 5 marks
A right triangle has positive legs \(x\) and \(x+6\). Derive an exact formula for its hypotenuse c.
Hint
The hypotenuse is a positive length.
Stage 9 - Q10 - 3 marks
A right triangle has two consecutive positive integer leg lengths and hypotenuse \(\sqrt{145}\) cm. Find the legs and prove that no other consecutive pair works.
Hint
The two similar squares should each be near 72.5.