Question

Arun, David and Raj each used a piece of wire measuring 32cm in length to make a shape. Arun made a square with a side of length 8cm. David made a rectangle with a length of 9cm. Raj made a rectangle with breadth of 10cm. Who made a shape with the greatest area?

Answer 1

The area of the quadrilateral increases as the lengths of the sides become

the same.

• Arun made the shape (square) with the greatest area

Reasons:

Length of the wire = 32 cm

Length of side of square Arun made, s = 8 cm

Perimeter of the square, P = 4 × 8 cm = 32 cm = Length of the wire

• Area of the square Arun made, A = s² = 8 cm × 8 cm = 64 cm²

Length of a side of the rectangle David made, L = 9 cm

Perimeter of the rectangle, P = 32 cm = 2·L + 2·B

Where;

B = The breadth of the rectangle

Therefore;

P =  32 cm = 2·L + 2·B = 2 × 9 cm + 2·B

2·B = 32 cm - 2 × 9 cm = 14 cm

B = 14 cm ÷ 2 = 7 cm

The breadth of the rectangle David made B = 7 cm

Therefore;

• The area of the rectangle David made, A = 9 cm × 7 cm = 56 cm²

Breadth of the rectangle Raj made, B = 10 cm

Therefore;

32 cm = 2·L + 2 × 10 cm

2·L = 32 cm - 2 × 10 cm = 12 cm

L = 12 cm ÷ 2 = 6 cm

The length of the rectangle Raj made, L = 6 cm

• Area of the rectangle Raj made, A = 10 cm × 6 cm = 60 cm²

Therefore;

• The square made by Arun that has an area of 64 cm² is the shape with the greatest area.

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