Question

# A rectangle has adjacent sides 8 cm and 6 cm. The perimeter of the square is equal to the perimeter of this rectangle find the difference between the area of the square and that of rectangle.

Solution

## Length (l) of the rectangle = 8 cm Breadth (b) of the rectangle = 6 cm Let the side of the square be a cm. Give: Perimeter of the square = perimeter of the rectangle $⇒$4 × a = 2 (l + b) $⇒$4 × a = 2 (8 + 6) $⇒$4 × a = 28 $⇒$a = 7 $⇒$Side of the square = 7 cm Difference between the areas of the square and the rectangle = area of the square − area of the rectangle                                                                                          = {(a)2 – lb} cm2                                                                                           = {(7)2 – (8)(6)} cm2                                                                                            = (49 – 48) cm2                                                                                            = 1 cm2 Thus, the difference is 1 cm2.MathematicsMathematics (Geometry)Standard IX

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