Question

Square of side A units, square of side B units and the rectangles each of length A units and breadth B units cover completely the square of side ____ units.

Answer 1

Answer:

In a square the length is equal to breadth.

Hence, area of a square = side × side

The number of 1 cm squares enclosed = 4

Area = 4 sq cm

4 = 2 × 2

Hence, area = side × side

The unit of sides and the corresponding uni

Step-by-step explanation:

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Answer 2

Given: Square of side A units, square of side B units and the 2 rectangles each of length A units and breadth B units cover completely a square.

To find: Length of the side of the square covered

Solution: Area of a square= side× side

Area of a square with side A units

= A× A

$= {A} ^{2}$

Area of a square with side B units

= B × B

$= {B}^{2}$

Area of a rectangle

= Length× Breadth

= A × B

Area of 2 such rectangles= 2AB

To cover the square completely, the area of the 2 squares and 2 rectangles should be equal to the area of the covered square.

Total area of the squares and the rectangles

=${A}^{2} + {B}^{2} + 2AB$

This can be written as:

${(A+B)}^{2}$

Therefore, area of the covered square is also equal to

${(A+B)}^{2}$

Let the length of the covered square be a.

Therefore,

${a}^{2} = {(A+B)}^{2}$

=> a = A+B

Therefore, the length of the side of the square is A+B units.