Question

find the area of a rectangular plot. one side of which is 48m and its diagnol is 50m​

Answer 1

★ How to do :-

Here, we are given with a rectangle whose length measures 48 metres and one of it's diagnol measures 50 metres. We are asked to find the area of that rectangle. To find the area of a rectangle, we are required with the length and breadth of the rectangle. But, in this question we aren't given with the measurement of the breadth. So, first we should find the measurement of breadth by the concept called as Pythagoras theorem. This can be used to find the breadth. Later, we can find the area of the rectangle by using th e formula that is used to calculate the area of a particular figure. So, let's solve!!

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➤ Solution :-

Breadth of the rectangle :-

${\sf \leadsto {AB}^{2} + {AD}^{2} = {BD}^{2}}$

Substitute the given values.

${\sf \leadsto {48}^{2} + {AD}^{2} = {50}^{2}}$

Find the square numbers of both numbers given.

${\sf \leadsto 2304 + {AD}^{2} = 2500}$

Shift the number 2304 from LHS to RHS, changing it's sign.

${\sf \leadsto {AD}^{2} = 2500 - 2304}$

Subtract the values on RHS.

${\sf \leadsto {AD}^{2} = 196}$

Remove square on LHS and insert square root on RHS.

${\sf \leadsto AD = \sqrt{196}}$

Find the square root of 196 to find the value of breadth

${\sf \leadsto AD = 14}$

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Now, let's find the area of the rectangle.

Area of the rectangle :-

${\sf \leadsto \underline{\boxed{\sf Length \times Breadth}}}$

Substitute the given values.

${\sf \leadsto 48 \times 14}$

Multiply the numbers to get the answer.

${\sf \leadsto {672 \: metres}^{2}}$

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${\red{\underline{\boxed{\bf So, \: the \: area \: of \: the \: rectangle \: is \: {672m}^{2}.}}}}$

Answer 2

$length^2+ breadth^2=diagonal^2 \\ \\So breadth=\sqrt{50^2−48^2} \\ \\ Breadth=14m \\ Area=48×14=672m^2$