Two plot of land have same perimeter. One is a square of side 60m while other is a rectangle, whose breath is 1.5 dam. which plot has greater area and by how much?
.answer is = Area of square plot greater by 2025 squad m.
.show me expllenation.
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Given:-
- Two plot of land have same perimeter.
- One is a square with side 60 m
- The other is a rectangle with breadth = 1.5 dam = 15 m
To Find:-
- Which plot has greater area and by how much.
Solution:-
Let us first find the perimeter of the square.
We know,
✭ Perimeter of square = 4 × side sq.units.
Hence,
Perimeter of the square field = 4 × 60 = 240 cm.
ATQ,
Perimeter of the square field = Perimeter of rectangular field.
We know,
✭ Perimeter of rectangle = 2(Length + Breadth)
Hence,
240 = 2(L + 15)
⇒240/2 = L + 15
⇒120 = L + 15
⇒L = 120 - 15
⇒L = 105 m
Now,
Let us find the area of rectangular plot and Square plot one by one.
For Rectangular plot,
We know,
✭ Area of rectangle = (Length × Breadth) sq.units
Hence,
Area of plot = 105 × 15
⇒ Area of plot = 1575 m²
For Square plot,
We know,
✭ Area of square = (side)²
Hence,
Area of plot = (60)²
⇒Area of the plot 3600 m²
Here we can clearly see that
Area of square plot > Area of rectangular plot.
Difference between the area of both the plots:-
= 3600 - 1575 = 2025 m²
∴ The area of the square plot is greater than the area of the rectangular plot by 2025 m².
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