Math  /  Geometry

QuestionLevel 1 Question 1 Use what you know about Pythagoras' Theorem to write an equation which describes the relationship between the sides of this triangle. Simplify and solve your equation.
Question 2 A triangle has a base length of (x1)cm(x-1) \mathrm{cm} and a height of (x+1)cm(x+1) \mathrm{cm}. Find its height if it has an area of 7 cm27 \mathrm{~cm}^{2}
Question 3 A rectangle has perimeter 20 cm and area 21 cm221 \mathrm{~cm}^{2}. What are its dimensions, in centimetres? (A) 1 and 20 (B) 4 and 6 (C) 9 and 2 (D) 3 and 7 (E) 6 and 3123 \frac{1}{2}
Question 4 The formula for the number of diagonals, NN, of a polygon with nn sides is N=n(n3)2N=\frac{n(n-3)}{2}. How many diagonals would a polygon with 23 sides have?

Studdy Solution
Use the diagonal formula for a polygon:
Given n=23n = 23,
N=23(233)2 N = \frac{23(23-3)}{2} N=23×202 N = \frac{23 \times 20}{2} N=4602 N = \frac{460}{2} N=230 N = 230
The polygon with 23 sides has 230 diagonals.

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