Free examples and worked answers. No account needed.
Practise the method.
Linked triangles and composite problems
Linked triangles and composite problems
Example 1
Two right triangles share a perpendicular height 30cm. Their hypotenuses are 34cm and 50cm. Their bases lie on opposite sides of the height. Find the total outer base x, in cm.
Linked right trianglesDiagram not to scaleShow worked answer
Answer: 56
Left base =√342−302=16.
Right base =√502−302=40.
Add: 16+40=56cm.
Example 2
Two right triangles share a perpendicular height 20cm and have hypotenuses 25cm and 29cm. Their bases lie on opposite sides of the height. Find the combined area, in cm2.
Linked right trianglesDiagram not to scaleShow worked answer
Answer: 360
The bases are √252−202=15 and √292−202=21.
Combined area = ½ ×(15+21)×20=360cm2.
Example 3
An isosceles triangle has equal sides 30cm and base 36cm. Find its perpendicular height x, in cm.
Linked right trianglesDiagram not to scaleShow worked answer
Answer: 24
The height bisects the base into 18cm halves.
Height =√302−182=24cm.
Put it into practice.
Sign in to choose a set, get feedback and keep your progress.