Question

Two plot of land have the same perimeter one is square of side 64m and the other is a rectangle of length 70m find the breath of the rectangular plot .which plot has the greater area and by how much?

Answer 1

Answer :

Breadth of rectangle = 58 m

Square plot has greater area by 36 m²

$\rule{100}2$

Solution with explanation :

It is given that,

Plot 1 :

• Square shaped with side, 64 m

Plot 2 :

• Rectangular shaped, length = 70 m

We have to find breadth of the rectangle and the plot which has greater area and also the measure by which plot 1 is greater than plot 2.

Now,

$\sf Perimeter\:of\:square=4\times side$

$\sf = 4\times 64$

$\sf = 256\:m$

Also, perimeter of plot 1 is equal to the perimeter of plot 2.

∵ Perimeter of Rectangle = 2 ( length × breadth )

Now,

$\sf 256 = 2 ( 70 + breadth )$

$\sf 256 = 140 + 2\times breadth$

$\sf 2\times breadth = 256 - 140$

$\sf 2\times breadth = 116$

$\sf b = \dfrac{116}{2}$

$\sf\therefore b = 58$

we know that,

$\sf Area\:of\:square= (side)^2$

Substitute the value. we get,

= ( 64 )²

= 4096 m²

Now,

∵ Area of rectangle = length × breadth.

So, substitute the values of length and breadth. We get,

= 70 × 58

= 4060 m²

On comparing the areas of both the plots, it is clear that the area of square plot ( 1 ) is greater than rectangular plot.

To find the difference,

= 4096 m² - 4060 m²

= 36 m²

Hence, square plot is greater than rectangular plot by 36 m².

$\rule{200}2$