Year 11
Space diagonals, tangents and combined lengths
Free examples and worked answers. No account needed.
Start practisingLoading personal best… Practise the method.
Example 1
A cuboid has space diagonal 65cm. Two edges are x and (34)xcm; the third is 60cm. Find x.
CuboidDiagram not to scaleShow worked answer
Answer: 15
- x2+((34)x)2+602=652.
- Hence (925)x2=625, giving the positive root x=15cm.
Example 2
A right triangle has legs xcm and 12cm. Its hypotenuse is (x+2)cm. Find x.
Right triangleDiagram not to scaleShow worked answer
Answer: 35
- Pythagoras gives x2+122=(x+2)2.
- Cancel x2 and solve 4x+4=144, obtaining x=35.
Example 3
A cuboid has space diagonal 65cm. Two edges are x and (34)xcm; the third is 60cm. Find x.
CuboidDiagram not to scaleShow worked answer
Answer: 15
- x2+((34)x)2+602=652.
- Hence (925)x2=625, giving the positive root x=15cm.