Question

11. Length of a rectangle is 16 cm less than twice its breadth. If the perimeter of the rectangle is 100 cm, find its length and breadth.​

Answer 1

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$\huge{\underline{\underline{\sf{\blue{SOLUTION:-}}}}}$

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$\sf{\underline{\green{AnswEr:-}}}$

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• Breadth of rectangle = 22 Cm
• Length of rectangle = 28 Cm

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$\sf{\underline{\green{Given:-}}}$

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• Length of a rectangle is 16 cm less than twice its breadth. If the perimeter of the rectangle is 100 cm.

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$\sf{\underline{\green{Find:-}}}$

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• Breath of rectangle = ?
• Length of rectangle = ?

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$\sf{\underline{\green{Explanation:-}}}$

Let the breadth be y.

$\:\:\:\:\dag\bf{\underline{\underline \red{Then:-}}}$

• Length = 2y - 16 Cm

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$\:\:\:\:\dag\bf{\underline{\underline \red{Now:-}}}$

$\sf\underline{\purple{\:\:\: Perimeter = 2 \times (Length + Breadth)\:\:\:}}$

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$\sf{Perimeter = 2 \times (2y + y - 16)}$

$\sf{Perimeter = 2 \times (3y - 16)}$

$\sf{Perimeter = 6y - 32}$

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$\sf{\underline\pink{A.T.Q:-}}$

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$\longrightarrow \sf {6y - 32 = 100}$

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$\longrightarrow \sf {6y = 100 + 32}$

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$\longrightarrow \sf {6y = 132}$

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$\longrightarrow \sf {y = \cancel\dfrac{132}{6} }$

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$\longrightarrow \sf {y = 22}$

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$\:\:\:\:\dag\bf{\underline{\underline \red{Hence:-}}}$

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• Breath of rectangle = 22 Cm

• Length of rectangle = 2 × 22 - 16
• Length of rectangle = 44 - 16
• Length of rectangle = 28 Cm

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$\rule{200}{2}$