Properties of Quadrilaterals to Solve Equations

Question	Answer
The length of the rectangle is 2x+5 The width of the rectangle is 3x-2 Image: Solving Algebraic Problems (image/png)	The perimeter of the rectangle is 46cm
Find the value of x 1) What do I have to do? - Read the question through twice. Highlight or underline the important pieces of information in the question	2) What information do I need? - The key word in the question is perimeter. - The question asks to find the value of x. The answer might be a whole number or a fraction or decimal
3) What information don't I need? Everything in this question is relevant to working out the answer	4) What maths can I do?
Step A: Opposite sides in a rectangle are equal Write on the lengths (expressions) of the other sides on your diagram Image: Solving Algebraic Problems 2 (image/png)	Step B: The perimeter of a shape is found by adding up all the sides. Find an expression for the perimeter: (2x + 5) + (3x - 2) + (2x +5) + (3x - 2) = 10x + 6
Step C: The perimeter of the rectangle is 46cm, therefore: 10x + 6 = 46	Step D: Solve this equation to find x: 10x + 6 = 46 Move the 6 across: 10x = 46 - 6 (It becomes negative and vice versa) 10x = 40 Then divide 40 by 10 x = 4
5) Is my solution correct? Check the answer by substituting the value of x into the length and width. The length of the rectangle is: 2x+5 If x=4 then 2x4+5 = 13cm	The width of the rectangle is: 3x-2 If x=4 then 3x4-2 = 10cm Check the original figure for the perimeter is reached by adding up all four sides: 13+10+13+10 = 46

Resource summary

	Created by Liffey Farrell about 7 years ago