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8 cm

x. x. x. x. A picture frame measures 8 cm by 12 cm. We wish to add a border of equal width around the frame. The area of the border must equal to the area of the frame. Determine the width of the border correct to one decimal place. Area of picture: 8 cm × 12 cm. = 96 cm 2.

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8 cm

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  1. x x x x A picture frame measures 8 cm by 12 cm. We wish to add a border of equal width around the frame. The area of the border must equal to the area of the frame. Determine the width of the border correct to one decimal place. Area of picture: 8 cm × 12 cm = 96 cm2 Area of picture and frame: 192 cm2 2x + 12 12 cm Let x = width of the picture frame. Equation: (2x + 8)(2x + 12) = 192 cm2 8 cm 4x2 + 24x + 16x + 96 = 192 4x2 + 40x + 96 – 192 = 0 2x + 8 4x2 + 40x – 96 = 0

  2. 4x2 + 40x – 96 = 0 4(x2 + 10x – 24) = 0 a = 1, b = 10 and c = – 24 x1 = 2 x2 = – 12 The width of the frame is 2cm.

  3. A bullet is fired vertically into the air at an initial velocity of 80 m/s. The height in metres is given by the h = 80t – 5t2. (t = sec.) Find the time it takes the bullet to reach 100 m. h = –5t2 + 80t 100= –5t2 + 80t 5t2 – 80t + 100= 0 5(t2 – 16t + 20)= 0 a = 1, b = –16 and c = 20 t = 1.2 sec or 14.8 sec

  4. x x x x A picture frame measures 15 cm by 25 cm. We wish to add a border of equal width around the frame. The area of the border must equal to the area of the frame. Determine the width of the border correct to one decimal place. Area of picture: 15 cm × 25 cm = 375 cm2 Area of picture and frame: 750 cm2 2x + 25 25 cm Let x = width of the picture frame. Equation: (2x + 15)(2x + 25) = 750 cm2 15 cm 4x2 + 50x + 30x + 375 = 750 4x2 + 80x + 375 – 750 = 0 2x + 15 4x2 + 80x – 375 = 0

  5. 4x2 + 80x – 375 = 0 a = 4, b = 80 and c = – 375 x1 = 3.9 x2 = – 23.92 The width of the frame is 3.9 cm.

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