## Exam-Style Questions on Pythagoras## Problems on Pythagoras adapted from questions set in previous Mathematics exams. |

## 1. | GCSE Higher |

\(ABC\) is a right-angled triangle.

John has a method for finding the length of \(AC\)

$$AC^2 = AB^2 - BC^2$$ $$AC^2 = 13^2 - 5^2$$ $$AC^2 = 169 - 25$$ $$AC^2 = 144$$ $$AC = \sqrt{144}$$ $$AC = 12$$John's answer of \(12cm\) is not correct.

(a) What mistake has he made with his method?

(b) Show the correct method and the correct answer to 3 significant figures.

## 2. | GCSE Higher |

An isosceles triangle shaped frame is made from four pieces of metal. The frame has a height of 8 metres and a base of length 12 metres.

The weight of the metal is 2.5kg per metre. Calculate the total weight of the metal in the frame.

## 3. | GCSE Higher |

The diagram shows a right-angled triangle and a semicircle. The straight side of the semicircle is the same length as the longest side of the triangle.

Work out the area of the semicircle.

Give your answer correct to 3 significant figures.

You must show all your working.

## 4. | GCSE Higher |

Four copies of a green right-angled triangle are used to enclose a yellow square.

Find the area of the yellow square if the longest side of the green triangle is of length \(a\) cm and the shortest side is \(b\) cm.

## 5. | GCSE Higher |

The gradient of the line joining the origin to the point A is \(\frac12\)

The distance between A and the origin is \(\sqrt{2205}\)

What are the coordinates of A?

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