find the area of a rectangular plot. one side of which is 48m and its diagnol is 50m About the author Alaia
Answer : Area of rectangular plot is 672m² Given : One side is 48m Diagonal is 50m To find : Area of rectangular plot Solution : As we know that, Pythagoras theorem, (AB)² = (AC)² + (BC)² 》(50)² = (48)² + (BC)² 》(BC)² = (50)² + (48)² 》(BC)² = 2500 – 2304 》(BC)² = 196 》BC = √ 196 》BC = 14cm So, Now we have to find the area of rectangular plot : Length is 48m Breadth is 14m As we know that, Area of rectangular plot = l × b Where, l is length and b is breadth 》 Area of rectangular plot = l × b 》48 × 14 》672m² Hence , Area of rectangular plot is 672m² Reply
[tex]{\purple{\underline{\underline{\mathsf{\mathbf{Solutíon:}}}}}}[/tex] ☯ Let ABCD be the rectangular plot. [tex]\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━[/tex] [tex]{ }[/tex] Then, AB ➻ 48 m AC ➻ 50 m [tex]{━━━━━━━━━━━━━━━━━━━}[/tex] [tex]\circleddash[/tex]Need to Find : The Area of the rectangular plot. [tex]{ }[/tex] According to Pythagoras Theorem, [tex]{ }[/tex] [tex]{\underline{\boxed{\mathsf{\mathbf{\red{(AC)}^{\red 2}\:{\red =\:{\red \red \red (\red A \red B \red )}}^{\red 2}\:{\red +\:\red (\red B \red C\red )}^{\red 2}}}}}}[/tex] [tex]{ }[/tex] [tex]\:\:\:\:\:\:\:\dashrightarrow\:\sf{(50)}^{2}\:=\:{(48)}^{2}\:+\:{(BC)}^{2}[/tex] [tex]{ }[/tex] [tex]\:\:\:\:\:\:\:\dashrightarrow\:\sf{(BC)}^{2}\:=\:{(50)}^{2}\:-\:{(48)}^{2}[/tex] [tex]{ }[/tex] [tex]\:\:\:\:\:\:\:\dashrightarrow\:\sf{(BC)}^{2}\:=\:{2500\:-\:2304}[/tex] [tex]{ }[/tex] [tex]\:\:\:\:\:\:\:\dashrightarrow\:\sf{(BC)}^{2}\:=\:{196}[/tex] [tex]{ }[/tex] [tex]\:\:\:\:\:\:\:\dashrightarrow\:\sf{BC\:=\:{\sqrt{196}}}[/tex] [tex]{ }[/tex] [tex]\:\:\:\:\:\:\:\dashrightarrow\:\sf{\bold{BC\:=\:14\:m}}[/tex] [tex]\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━[/tex] Hence, [tex]{ }[/tex] [tex]{\underline{\boxed{\mathsf{\mathbf{\red{The\:Area\:of\:the\:rectangle\:plot\:=\:l\:\times\:b}}}}}}[/tex] [tex]{ }[/tex] Where, [tex]{ }[/tex] L ➻ 48 m B ➻ 14 m [tex]{ }[/tex] Then, [tex]\:\:\:\:\:\:\:\succcurlyeq{\sf{48\:\times\:14}}[/tex] [tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\succcurlyeq{\sf{672\:m}^{2}}[/tex] [tex]{ }[/tex] [tex]\:\therefore\:{\underline{\sf{The\:Area\:of\:Rectangular\:Plot\:is\:{\textsf{\textbf{672\: m²}}}}}}.[/tex] [tex]{ }[/tex] [tex]\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━[/tex] [tex]{\bf{\sf{\pink{@ℐᴛᴢӇᴀᴘᴘʏҨᴜᴇᴇɴ࿐}}}}[/tex] Reply
Answer :
Given :
To find :
Solution :
As we know that, Pythagoras theorem,
》(50)² = (48)² + (BC)²
》(BC)² = (50)² + (48)²
》(BC)² = 2500 – 2304
》(BC)² = 196
》BC = √ 196
》BC = 14cm
So,
Now we have to find the area of rectangular plot :
As we know that,
Where, l is length and b is breadth
》 Area of rectangular plot = l × b
》48 × 14
》672m²
Hence , Area of rectangular plot is 672m²
[tex]{\purple{\underline{\underline{\mathsf{\mathbf{Solutíon:}}}}}}[/tex]
☯ Let ABCD be the rectangular plot.
[tex]\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━[/tex]
[tex]{ }[/tex]
Then,
[tex]{━━━━━━━━━━━━━━━━━━━}[/tex]
[tex]\circleddash[/tex]Need to Find : The Area of the rectangular plot.
[tex]{ }[/tex]
According to Pythagoras Theorem,
[tex]{ }[/tex]
[tex]{ }[/tex]
[tex]\:\:\:\:\:\:\:\dashrightarrow\:\sf{(50)}^{2}\:=\:{(48)}^{2}\:+\:{(BC)}^{2}[/tex]
[tex]{ }[/tex]
[tex]\:\:\:\:\:\:\:\dashrightarrow\:\sf{(BC)}^{2}\:=\:{(50)}^{2}\:-\:{(48)}^{2}[/tex]
[tex]{ }[/tex]
[tex]\:\:\:\:\:\:\:\dashrightarrow\:\sf{(BC)}^{2}\:=\:{2500\:-\:2304}[/tex]
[tex]{ }[/tex]
[tex]\:\:\:\:\:\:\:\dashrightarrow\:\sf{(BC)}^{2}\:=\:{196}[/tex]
[tex]{ }[/tex]
[tex]\:\:\:\:\:\:\:\dashrightarrow\:\sf{BC\:=\:{\sqrt{196}}}[/tex]
[tex]{ }[/tex]
[tex]\:\:\:\:\:\:\:\dashrightarrow\:\sf{\bold{BC\:=\:14\:m}}[/tex]
[tex]\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━[/tex]
Hence,
[tex]{ }[/tex]
[tex]{ }[/tex]
Where,
[tex]{ }[/tex]
[tex]{ }[/tex]
Then,
[tex]\:\:\:\:\:\:\:\succcurlyeq{\sf{48\:\times\:14}}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\succcurlyeq{\sf{672\:m}^{2}}[/tex]
[tex]{ }[/tex]
[tex]\:\therefore\:{\underline{\sf{The\:Area\:of\:Rectangular\:Plot\:is\:{\textsf{\textbf{672\: m²}}}}}}.[/tex]
[tex]{ }[/tex]
[tex]\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━[/tex]
[tex]{\bf{\sf{\pink{@ℐᴛᴢӇᴀᴘᴘʏҨᴜᴇᴇɴ࿐}}}}[/tex]