1. Further Quadratic Problems
The diagram shows a trapezium. The trapezium has an area of 17 𝑐𝑚 2 . Work out the value of 𝑥 to 3 significant figures.
How can we begin?

2. Further Quadratic Problems
The diagram shows a trapezium. The trapezium has an area of 17 𝑐𝑚 2 . Work out the value of 𝑥 to 3 significant figures.
Write an expression for the area of the trapezium

3. Further Quadratic Problems
The diagram shows a trapezium. The trapezium has an area of 17 𝑐𝑚 2 . Work out the value of 𝑥 to 3 significant figures.
Change this expression into an equation using the information given

4. Further Quadratic Problems
The diagram shows a trapezium. The trapezium has an area of 17 𝑐𝑚 2 . Work out the value of 𝑥 to 3 significant figures.
Change this expression into an equation using the information given

5. 1 2 𝑥+𝑥+7 ×2𝑥=17
Try in your pairs and on your table to show that this equation can be simplified to:
2𝑥 2 +7𝑥−17=0

6. How can we solve: 2𝑥 2 +7𝑥−17=0
𝒂 = 2, 𝒃 = 7, 𝒄 = -17
𝑥= −𝒃± 𝒃 2 −4𝒂𝒄 2𝒂
𝑥= −(𝟕)± (𝟕) 2 −4×𝟐×(−𝟏𝟕) 2×𝟐 𝑥=
𝑥=−

7. Relate these solutions back to the problem
The diagram shows a trapezium. The trapezium has an area of 17 𝑐𝑚 2 . Work out the value of 𝑥 to 3 significant figures. 𝑥=
𝑥=−
∴𝒙=𝟏.𝟔𝟓

8. Your Turn:
1. The diagram shows a trapezium of area 119 𝑐𝑚 2 All measurements are in centimetres. Work out the value of x to 3 sf.
2. The diagram shows a trapezium of area 42 𝑐𝑚 2
All measurements are in centimetres.
Calculate the perimeter of the trapezium.

9. Further Quadratic Problems
A right-angled triangle has sides of length 𝑥 cm, (𝑥+3) cm and (𝑥 +2) cm Work out the value of 𝑥 to 3 significant figures
How can we begin?
𝑥 +3 𝑥
𝑥+2

10. Further Quadratic Problems
A right-angled triangle has sides of length 𝑥 cm, (𝑥+3) cm and (𝑥 +2) cm Work out the value of 𝑥 to 3 significant figures
Write an equation using Pythagoras’ theorem on your whiteboards
𝑥 +3 𝑥
𝑥+2

11. (𝑥+3 ) 2 =(𝑥+2 ) 2 + 𝑥 2
Try in your pairs and on your table to show that this equation can be simplified to:
𝑥 2 −2𝑥−5=0

12. How can we solve: 𝑥 2 −2𝑥−5=0
𝒂 = 1, 𝒃 = -2, 𝒄 = -5
𝑥= −𝒃± 𝒃 2 −4𝒂𝒄 2𝒂
𝑥= −(−𝟐)± (−𝟐) 2 −4×𝟏×(−𝟓) 2×𝟏 𝑥= 𝑥=
𝑥=−

13. Relate the solutions back to the problem
A right-angled triangle has sides of length 𝑥 cm, (𝑥+2) cm and (𝑥 +3) cm Work out the value of 𝑥 to 3 significant figures 𝑥=
𝑥=−
𝑥 +3 𝑥
∴𝑥=3.45
𝑥+2

14. Further Quadratic Problems
The diagram shows a rectangle. The perimeter of the rectangle is 20 cm. Work out the value of 𝑥 to 3 significant figures.

15. Further Quadratic Problems
The diagram shows one disc with centre A and radius 4 cm and another disc with centre B with radius 𝑥 cm. The two discs fit exactly into a rectangle with dimensions 10 cm and 9 cm as shown. Work out the value of 𝑥 correct to 3 significant figures.