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

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

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2 thoughts on “find the area of a rectangular plot. one side of which is 48m and its diagnol is 50m​”

  1. 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

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  2. [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]

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