Math, asked by ansarik6454, 11 months ago

Find the area of a rectangular plot,oneside of which measures 35m and the daiagonal is 37m

Answers

Answered by Anonymous
22

Reference of image is in diagram :

\setlength{\unitlength}{0.78cm}\begin{picture}(12,4)\thicklines\put(5.6,9.1){$A$}\put(5.5,5.8){$B$}\put(11.1,5.8){$C$}\put(11.05,9.1){$D$}\put(4.5,7.5){$?$}\put(8.1,5.3){$35\:m$}\put(11.5,7.5){$?$}\put(8.1,9.5){$35\:m$}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(6,6){\line(5,3){5}}\end{picture}

 \rule{100}2

\bullet\frak{Given}\begin{cases}\sf{AD = 35cm}\\\sf{BD = 37cm}\end{cases}

\bullet\sf\ We\: have \: to \: find \: area \: of \: rectangular \: plot

\underline{\dag\:\textsf{Basic \: concept \: used \: in \: question:}}

• Each angle of rectangle is of 90°

Also; we use Pythagorus theorem [sum of squares of two sides of a right angled triangle is equal to the third side].

Area of rectangle = length × Breadth

\underline{\dag\:\textsf{Let's \: head \: to \: the \: question \: now:}}

\normalsize\star\sf\ In \: right \:  \triangle ABC -

\normalsize\ : \implies\sf\ (Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2 \\ \\ \normalsize\ : \implies\sf\ (BD)^2 = (AD)^2 + (AB)^2 \\ \\ \normalsize\ : \implies\sf\ (37)^2 = (35)^2 + (AB)^2 \\ \\ \normalsize\ : \implies\sf\ 1369 = 1225 + AB^2 \\ \\ \normalsize\ : \implies\sf\ AB^2 = 144 \\ \\ \normalsize\ : \implies\sf\ AB = \sqrt{144} = 12

\therefore\underline{\textsf{Hence, \: the \: length \: of \:  AB = 12cm }}

 \rule{100}2

\normalsize\star\sf\ Now; \: Area \: of \: rectangular \: plot -

\normalsize\ : \implies\sf\ Area \: of \: plot \: = \: Length \times\ Breadth \\ \\ \normalsize\ : \implies\sf\ Area \: of \: plot \: = AB  \times\ AD \\ \\ \normalsize\ : \implies\sf\ 35 \times\ 12 \\ \\ \normalsize\ : \implies\sf\ 420m^2

\normalsize\ : \implies{\boxed{\sf{Area \: of \: plot = 420  \: m^2}}}

 \rule{100}2

\boxed{\begin{minipage}{8cm}\bf\underline{Some important formula related to it :}\\ \\ \textsf{$\bullet\ Perimeter \:  of  \: rectangle = 2(length + breadth)$}\\ \textsf{$\bullet\ Area \: of \: rectangle = length \times\ breadth$} \\ \textsf{$\bullet\ Area \: of \: square = (side)^2$} \\ \textsf{$\bullet\ Perimeter \: of \: square = 4 \times\ side$}  \\ \textsf{$\bullet\ Area \: of \: circle  = \pi r^2$}\\ \textsf{$\bullet\ Circumference \: of \: circle = 2 \pi r$}\\ \textsf{$\bullet\ Area \: of \: triangle= \sqrt{s(s-a)(s-b)(s-c)}$}\\ \textsf{$\bullet\ Perimeter \: of \: triangle = sum \: of \:  sides$}\end{minipage}}

Answered by Anonymous
58

Answer:- 420 m ²

Step-by-step explanation:

Given: Length of one side is 35 metre

  • Length of diagonal is 37 metre

To find: Area of rectangle ABCD

We know that each angle of a rectangle is 90°

In right angle ∆BCD , BC = 35m and DB= 37m

So, By Pythagoras theorem,

\large\implies{\sf }(DB)² = (BC)² + (DC)²

\large\implies{\sf }DB² = 35² + DC²

\large\implies{\sf } 37² =35² + DC²

\large\implies{\sf }1369 = 1225 + DC²

\large\implies{\sf }13691225 = DC²

\large\implies{\sf }144 = DC²

\large\implies{\sf } 144 = DC

\large\implies{\sf }12 metre = DC

As we know that the opposite sides of a rectangle are equal to each other

So, AB= DC=12 metres and AD= BC = 35 metres

  • Area of rectangle= Length x Breadth

Length = AB = DC = 12 m

Breadth= AD = BC = 35 m

So, Area of rectangle ABCD = 12 x 35 = 420

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