Mr Lee had a piece of wire 26y cm long. He used the wire to form a rectangle, with length and breadth measuring 2y cm and 2y cm.

  1. (a)

    Express the length of the remaining wire in terms of y.

    Answer : (a) ___

  2. (b)

    Mr Lee used the remaining wire to make a square. If y = 4, what was the length of one side of the square?

    Answer : (b) ___

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Worked solution

6(a)

1. Calculate the perimeter of the rectangle formed

Perimeter of rectangle =2×(2y+2y)=2×4y=8y= 2 \times (2y + 2y) = 2 \times 4y = 8y cm

2. Find the length of the remaining wire

Remaining wire =26y−8y=18y= 26y - 8y = 18y cm

Answer

18y18y

6(b)

1. Find the length of the remaining wire from part (a)

Length of remaining wire =26y−(2y+2y+2y+2y)=26y−8y=18y= 26y - (2y + 2y + 2y + 2y) = 26y - 8y = 18y cm

2. Substitute $y = 4$ into the expression for the remaining wire

Length of remaining wire =18(4)=72= 18(4) = 72 cm

3. Calculate the length of one side of the square

Length of one side =72÷4=18= 72 \div 4 = 18 cm

Answer

1818 cm

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