Question

Two plots of land have same perimeter . One is a square of side 60m,while the other is a rectangle whose breadth is 1.5dam. Which plot has greater area and by how much?

Answer 1

${\large{\pmb{\sf{\underline{Given \; that...}}}}}$

• Two plots are given.
• Rectangular and square plot.
• Side of square plot = 60 m.
• B of rectangular plot = 1.5 dam

${\large{\pmb{\sf{\underline{To \; find...}}}}}$

• Which plot has greater area and by how much?

${\large{\pmb{\sf{\underline{Solution...}}}}}$

• Square plot has more area that rectangular plot by 2025 m²

${\large{\pmb{\sf{\underline{Using \; concepts...}}}}}$

• Covert dam into metres.
• Perimeter of square formula.
• Perimeter of rectangle formula.
• Area of square formula
• Area of rectangle formula

${\large{\pmb{\sf{\underline{Using \; formulas...}}}}}$

${\small{\underline{\boxed{\sf{\circ \: 1 \: dam \: = 10 \: m}}}}}$

${\small{\underline{\boxed{\sf{\circ \: Perimeter \: of \: square \: = 4 \times side}}}}}$

${\small{\underline{\boxed{\sf{\circ \: Area \: of \: square \: = side \times side}}}}}$

${\small{\underline{\boxed{\sf{\circ \: Perimeter \: of \: rectangle \: = 2(l+b)}}}}}$

${\small{\underline{\boxed{\sf{\circ \: Area \: of \: rectangle \: = Length \times Breadth}}}}}$

${\large{\pmb{\sf{\underline{Full \; Solution...}}}}}$

~ As it is given that there are two units and both are different different so we have to covert any one of them into another. Let us convert!

${\small{\underline{\boxed{\sf{\circ \: 1 \: dam \: = 10 \: m}}}}}$

${\sf{:\implies 1 \: dam \: = 10 \: m}}$

${\sf{:\implies 1.5 \times 10}}$

${\sf{:\implies 15 \: m}}$

Henceforth, 15 metres is the breadth of the rectangle here.

$\begin{gathered}\begin{gathered}\begin{gathered} \sf Length \: is \: ? \: \: \: \: \: \: \: \: \: \: \: \\ \begin{gathered}\begin{gathered}\boxed{\begin{array}{}\bf {\red{}}\\{\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}\\ { \sf{ }}\\ { \sf{ }} \\ \\ { \sf{ }}\end{array}}\end{gathered}\end{gathered} \sf Breadth \: is \: 15 \: m \end{gathered}\end{gathered}\end{gathered}$

~ As it is given that the perimeter of square plot and rectangular plot is equal. Henceforth, let us find the area of square plot first!

${\small{\underline{\boxed{\sf{\circ \: Perimeter \: of \: square \: = 4 \times side}}}}}$

${\sf{:\implies 4 \times 60}}$

${\sf{:\implies 240 \: m}}$

Henceforth, perimeter of square plot is 240 metres.

${\small{\underline{\boxed{\sf{\circ \: Perimeter \: of \: square \: = Perimeter \: of \: rectangle}}}}}$

${\sf{:\implies 240 \: = 2(l+b)}}$

${\sf{:\implies 240 \: = 2(15+b)}}$

${\sf{:\implies 240 \: = 30 + 2b}}$

${\sf{:\implies 240-30 = 2b}}$

${\sf{:\implies 210 = 2b}}$

${\sf{:\implies 210/2 = b}}$

${\sf{:\implies 105 \: = b}}$

${\sf{:\implies b \: = 105 \: m}}$

Henceforth, 105 m is the breadth of the rectangular plot.

~ Now finding area of square!

${\small{\underline{\boxed{\sf{\circ \: Area \: of \: square \: = side \times side}}}}}$

${\sf{:\implies Area \: of \: square \: = side \times side}}$

${\sf{:\implies Area \: of \: square \: = 60 \times 60}}$

${\sf{:\implies Area \: of \: square \: = 3600 \: m^{2}}}$

Henceforth, 3600 m² is the area of the square.

~ Now let's find the area of rectangle!

${\small{\underline{\boxed{\sf{\circ \: Area \: of \: rectangle \: = Length \times Breadth}}}}}$

${\sf{:\implies Area \: of \: rectangle \: = Length \times Breadth}}$

${\sf{:\implies Area \: of \: rectangle \: = 15 \times 105}}$

${\sf{:\implies Area \: of \: rectangle \: = 1575 \: m^{2}}}$

Henceforth, 1575² is the area of rectangle.

~ Now let us see that whose area is more!

${\sf{:\implies 3600 \: is \: greater \: than \: 1575}}$

${\sf{:\implies Area \: of \: square \: is \: greater \: than \: Area \: of \: rectangle}}$

~ Now let's see that from much times that area of square plot is greater than area of rectangle.

${\sf{:\implies 3600-1575}}$

${\sf{:\implies From \: 2025 \: m \: sq. \: it \: is \: larger}}$