Question

In exchange for a square plot of land, one of whose side is 56m, a man wants to buy a rectangular plot 64m long and of the same area as that of square plot. Find the width of the rectangular plot

Answer 1

Given:

• In exchange for a square plot of land, one of whose side is 56m
• A man wants to buy a rectangular plot 64m long and of the same area as that of square plot

To Find:

• The breadth of the rectangular plot

Solution:

As we have been said that the square plot is to be replaced by the rectangular one, So let's firstly find the area of the square plot

– As we have said that the area of the rectangular and the square plots are the same so, let's find the breadth of the rectangle with the help of the length and area.

Now let's find the area of the square,

$\dashrightarrow \tt Area \; of \; a \; square = Side \times Side$

$\dashrightarrow \tt Area \; of \; the \; square = 56m \times 56m$

$\dashrightarrow \tt Area \; of \; the \; square = (56m)^2$

$\dashrightarrow \tt Area \; of \; the \; square = 3136m^2$

As  we know that the area of the square is equal to the area of the rectangular plot so, let's find the breadth of the rectangle now,

$\dashrightarrow \tt Area \; of \; a \; rectangle = L \times B$

$\dashrightarrow \tt 3136m^2 = Length \times 64m$

$\dashrightarrow \tt Lenght = \dfrac{3136}{64}$

$\dashrightarrow \tt Length = 49m$

Hence:

• The length the rectangular plot is 49m

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