Answer: Area will increase 56.25%.
Given: Each side is increased by a quarter.
To Find: The percentage increase in the area of a rectangle.
Step-by-step explanation:
Step 1: A rectangle is a two-dimensional (2D) form in which the four angles are all right angles and the opposite sides are parallel and equal to one another.
A rectangle's area (A) is calculated by multiplying its length ('x') by its breadth ('y'). Area of Rectangle is therefore equal to (xy) square units.
Step 2: Let the length of rectangle is x and breadth is y.
So, area of the rectangle = xy
If each side is increased by a quarter then new length of the sides are length will be [tex]x+\frac{x}{4} =\frac{5x}{4}[/tex] and width will be [tex]x+\frac{y}{4} =\frac{5y}{4}[/tex].
Now, new area of rectangle =
[tex]=\frac{5x}{4} \times \frac{5y}{4} \\\\=\frac{25}{16} xy\\\\=(1+\frac{9}{16})xy[/tex]
Step 3: Now percentage change = ((new area - area) ÷ area) x 100
[tex]= \frac{(1+\frac{9}{16})xy-xy}{xy} \times 100\\\\= \frac{(\frac{9}{16}xy)}{xy} \times 100\\\\=\frac{9}{16} \times 100\\\\=56.25[/tex]
Hence we can say that after increased by a quarter of the sides of a rectangle the area will increase 56.25%.
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