perimeter of rectangle is 120 cm if breath of the rectangle is 14 cm find its length and area of rectangle​

perimeter of rectangle is 120 cm if breath of the rectangle is 14 cm find its length and area of rectangle​

2 thoughts on “perimeter of rectangle is 120 cm if breath of the rectangle is 14 cm find its length and area of rectangle​”

  1. Given : The Perimeter of Rectangle is 120 cm & the Breadth of Rectangle is 14 cm .

    Exigency to find : Length and Area of Rectangle .

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    ❍ Let’s Consider the Length of Rectangle be x cm .

    ⠀⠀Finding Length of Rectangle :

    [tex]\dag\:\:\it{ As,\:We\:know\:that\::}\\[/tex]

    [tex]\qquad \dag\:\:\bigg\lgroup \sf{Perimeter _{(Rectangle)} \:: 2( l + b) }\bigg\rgroup \\\\[/tex]

    ⠀⠀Here l is the Length of Rectangle & b is the Breadth of Rectangle & we know the Perimeter of Rectangle is 120 cm

    ⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\[/tex]

    [tex]\qquad \longmapsto \sf 120 = 2( x + 14 ) \\ [/tex]

    [tex]\qquad \longmapsto \sf \cancel {\dfrac{120}{2}} = ( x + 14 ) \\ [/tex]

    [tex]\qquad \longmapsto \sf 60 = ( x + 14 ) \\ [/tex]

    [tex]\qquad \longmapsto \sf 60 – 14 = x \\ [/tex]

    [tex]\qquad \longmapsto \frak{\underline{\purple{\:x = 46 cm }} }\bigstar \\[/tex]

    Therefore,

    ⠀⠀⠀⠀⠀[tex]\therefore {\underline{ \mathrm {\:Length \:of\:Rectangle \:is\:\bf{46\:cm}}}}\\[/tex]

    ⠀⠀Finding Area of Rectangle :

    [tex]\dag\:\:\it{ As,\:We\:know\:that\::}\\[/tex]

    [tex]\qquad \dag\:\:\bigg\lgroup \sf{ Area_{(Rectangle)} \:: l \times b }\bigg\rgroup \\\\[/tex]

    ⠀⠀Here l is the Length of Rectangle & b is the Breadth of Rectangle

    ⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\[/tex]

    [tex]\qquad \longmapsto \sf Area = 46 \times 14 \\ [/tex]

    [tex]\qquad \longmapsto \frak{\underline{\purple{\:Area = 644 cm^2 }} }\bigstar \\[/tex]

    Therefore,

    ⠀⠀⠀⠀⠀[tex]\therefore {\underline{ \mathrm {\:Area \:of\:Rectangle \:is\:\bf{644\:cm^2}}}}\\[/tex]

    ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

    [tex]\large {\boxed{\sf{\mid{\overline {\underline {\star More\:To\:know\::}}}\mid}}}\\\\[/tex]

    [tex]\qquad \leadsto \sf Area_{(Rectangle)} = Length \times Breadth [/tex]

    [tex]\qquad \leadsto \sf Perimeter _{(Rectangle)} = 2 (Length + Breadth) [/tex]

    [tex]\qquad \leadsto \sf Area_{(Square)} = Side \times Side [/tex]

    [tex]\qquad \leadsto \sf Perimeter _{(Square)} = 4 \times Side [/tex]

    [tex]\qquad \leadsto \sf Area_{(Trapezium)} = \dfrac{1}{2} \times Height \times (a + b )[/tex]

    [tex]\qquad \leadsto \sf Area_{(Parallelogram)} = Base \times Height [/tex]

    [tex]\qquad \leadsto \sf Area_{(Triangle)} = \dfrac{1}{2} \times Base \times Height [/tex]

    [tex]\qquad \leadsto \sf Area_{(Rhombus)} = \dfrac{1}{2} \times Diagonal _{1}\times Diagonal_{2} [/tex]

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