On a squared grid paper (1 square = 1 square unit), make as many rectangles as you can Class 6

On a squared grid paper (1 square = 1 square unit), make as many rectangles as you can Class 6

Question 1.

On a squared grid paper (1 square = 1 square unit), make as many rectangles as you can whose lengths and widths are a whole number of units such that the area of the rectangle is 24 square units. Class 6

(а) Which rectangle has the greatest perimeter?

(b) Which rectangle has the least perimeter?

(c) If you take a rectangle of area 32 sq cm, what will your answers be?

Given any area, is it possible to predict the shape of the rectangle with the greatest perimeter as well as the least perimeter? Give examples and reasons for your answer.

Solution:

Do as directed. Rectangles can be of sides 24 and 1, 12 and 2, 8 and 3 and 6 and 4 units.

(a) Greatest perimeter will be 50 units of rectangle of sides 24 and 1 units.

(b) Least perimeter will be 20 units of rectangle of sides 6 and 4 units.

(c) For rectangle of area 32 sq units, rectangles can be of sides 32 and 1 units, 16 and 2 units, and 8 and 4 units. In that case, greatest perimeter of the rectangle will be 66 units and least perimeter of the rectangle will be 24 units. Given any area, it is possible to predict the shape of the rectangle with the greatest perimeter only if the lengths of its sides are in integral units, as we have done above in (a), otherwise we cannot predict the shape because the perimeter may be of any infinite length. So far as the case of least perimeter is concerned, it can be predicted that the rectangle will be of the shape of a square.

Question 2.

Check! whether the two triangles overlap each other exactly. Do they have the same area? Class 6

Solution:

Yes, yes.