Triangle ABC is similar to triangle APQ, with angle CBA equal to angle QPA and angle A common to both triangles. The lengths of sides AB, AP and PQ are 90 cm, 60 cm and 30 cm. Calculate the length of side BC.
To solve this problem, we can use the concept of similarity between triangles. Two triangles are similar if their corresponding angles are equal, and the corresponding sides are proportional.
Given that triangle ABC is similar to triangle APQ, we can set up a proportion using the corresponding side lengths:
AB / AP = BC / PQ
Substituting the given lengths:
90 cm / 60 cm = BC / 30 cm
Now we can solve for BC. To isolate BC, we can cross-multiply:
90 cm * 30 cm = 60 cm * BC
2700 cm^2 = 60 cm * BC
Divide both sides by 60 cm to solve for BC:
BC = 2700 cm^2 / 60 cm
Simplifying:
BC = 45 cm
Therefore, the length of side BC is 45 cm.