Question

Look at the rectangle. 2 cm 18 cm a) A square has the same area as the rectangle above. What is the side length of this square? + + Answer: b) A different square has the same perimeter as the rectangle above. What is the side length of this square? Diagram not drawn to scale Answer:​

Answer 1

a) side = 6 cm

b) side = 10 cm

Explanation:

Dimensions of a rectangle are 2 cm and 18cm.

`\boxed{\text{\bf Area of a rectangle = length * width}}\\\\`

= 2 * 18

= 36 cm²

It is given that the area of square is same as the area of the rectangle. We can find the side of the square by finding the square root of area.

a) Area of square = area of rectangle

side² = 36

side = √36

`\sf = √(6*6)\\\\\boxed{\sf side = 6 \ cm}`

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b) Another square has the perimeter like the rectangle.

Perimeter of rectangle = 2*(length + width)

= 2 *( 2 + 18)

= 2 * 20

= 40 cm

Perimeter of another square = 40 cm

4* side = 40

side = 40 ÷ 4

side = 10 cm