Further Quadratic Problems

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Presentation transcript:

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?

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

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

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

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

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=1.65037 𝑥=−5.15037

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=1.65037 𝑥=−5.15037 ∴𝒙=𝟏.𝟔𝟓

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.

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

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

(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

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=3.44949 𝑥=3.44949 𝑥=−1.44949

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=3.44949 𝑥=−1.44949 𝑥 +3 𝑥 ∴𝑥=3.45 𝑥+2

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.

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.