  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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