Pythagoras Theorem - 4 Examples

In this course, you will work through four carefully selected examples to learn how to apply the Pythagoras’ Theorem accurately and effectively. You will understand when the theorem can be used, how to identify the correct sides in a right-angled triangle, and how to solve for unknown lengths step by step, helping you avoid common mistakes and build confidence in problem-solving.

Related Lessons:
  1. S2 Pythagoras Theorem

Pythagoras Theorem Example 1

PQR is a triangle in which \(∠𝑃𝑄𝑅=90°\). Given that PR=3cm, \(QR=(3x)cm\) and \(PQ=(x+1)cm\),

  1. Form an equation in \(x\) and show that it reduces to \(5𝑥^2+𝑥−4=0\)
  2. Solve this equation and find the length of QR

Pythagoras Theorem Example 2

The shadow of a lamp post and that of a girl overlaps one another. The girl is 1.6m tall and her shadow DP is 6.4m long. The lamp post is 44.8m away from the girl. Given that triangle PAB is similar to triangle PCD, find
  1. the height of the lamp post.
  2. distance from the top of the lamp post to the girl’s head (Length of AC)

Pythagoras Theorem Example 3

In the figure, PQ is perpendicular bisector of the chord HK. If HK=3cm and PQ=3.2cm, calculate the radius of the circle.

Pythagoras Theorem Example 4

Given that AB=8cm, BC=6cm, AE=4cm and AD=DC, find the value of
  1. AD
  2. DE
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Related Lessons:

  1. S2 Pythagoras Theorem

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