# 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.

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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