Question

the perimeter of a rectangle is 82 metre and its area is 400m2 .the breadth of a rectengle willbe

Answer 1

give any thing length or breadth so I Will find

Answer 2

$\large\underline\pink{Given:-}$

• The perimeter of a rectangle is 82 m

it's area is 400 m²

$\large\underline\pink{To find:-}$

• Fine the breadth of rectangle ....?

$\large\underline\pink{Solutions:-}$

• Let breadth of rectangle be b.

Perimeter of a rectangle = 2(l + b)

$\: \: \: \: \: \leadsto \: \: {2} \: {({l} \: + \: {b})} \: \: = \: \: {82}$

$\: \: \: \: \: \leadsto \: \: {l} \: + \: {b} \: \: = \: \: \cancel{\frac{82}{2}}$

$\: \: \: \: \: \leadsto \: \: {l} \: + \: {b} \: \: = \: \: {41}$

$\: \: \: \: \: \leadsto \: \: {l} \: \: = \: \: {41} \: - \: {b}$

Area of rectangle = l × b

$\: \: \: \: \: \leadsto \: \: {l} \: \times \: {b} \: \: = \: \: {400}$

$\: \: \: \: \: \leadsto \: \: {({41} \: - \: {b})} \: \times \: {b} \: \: = \: \: {400}$

$\: \: \: \: \: \leadsto \: \: {41b} \: - \: {b}^{2} \: \: = \: \: {400}$

$\: \: \: \: \: \leadsto \: \: {b}^{2} \: - \: {41b} \: + \: {400} \: \: = \: \: {0}$

$\: \: \: \: \: \leadsto \: \: {b}^{2} \: - \: {25b} \: - \: {16b} \: + \: {400} \: \: = \: \: {0}$

$\: \: \: \: \: \leadsto \: \: {b} \: {({b} \: - \: {25})} \: - \: {16} \: {({b} \: + \: {25})} \: \: = \: \: {0}$

$\: \: \: \: \: \leadsto \: \: {({b} \: - \: {25})} \: \: {16} \: {({b} \: - \: {16})}$

$\: \: \: \: \: \leadsto \: \: {b} \: \: = \: \: {16} \: m \: \: \: \: {b} \: \: = \: \: {25} \: m$

so, length, l = 41 - b

⟹ 41 - 16

⟹ 25m

Hence, The breadth and length of rectangle is 16m and 25m.

$\large\underline\pink{More \: Information:-}$

• Perimeter of a rectangle = 2(l + b)
• Area of a rectangle = l × b
• Diagonal of a rectangle = √l² + b²