Question

1. The perimeter of a square is 48 cm. The area
of a rectangle is 4 cm less than the area of the
square. If length of the rectangle is 14 cm, then
its perimeter is​

Answer 1

AnswEr :

• Perimeter of Square = 48 cm
• Area of Rectangle is 4 cm² less than Area of Square.
• Length of Rectangle = 14 cm

• PERIMETER⠀OF⠀SQUARE :

↠ Perimeter of Square = 4 × Side

↠ 48 cm = 4 × Side

• Dividing both term by 4

↠ Side = 12 cm

________________

• Area of Square :

↠ Area of Square = (Side)²

↠ Area of Square = (12 cm)²

↠ Area of Square = (12 cm × 12 cm)

↠ Area of Square = 144 cm²

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• Area of Rectangle :

↠ Area of Rectangle = Length × Breadth

↠ Area of Square – 4 = 14 cm × Breadth

↠ 144 cm² – 4 cm² = 14 cm × Breadth

↠ 140 cm² = 14 cm × Breadth

• Dividing both term by 14 cm

↠ Breadth = 10 cm

________________

• PERIMETER⠀OF⠀RECTANGLE :

↠ Perimeter = 2(Length + Breadth)

↠ Perimeter = 2(14 cm + 10 cm)

↠ Perimeter = 2 × 24 cm

↠ Perimeter = 48 cm

∴ Perimeter of Rectangle will be 48 cm.

Answer 2

$\bf{\Huge{\boxed{\tt{\red{ANSWER\::}}}}}$

48cm

$\bf{\Large{\underline{\bf{Given\::}}}}$

The perimeter of a square is 48cm. The area of rectangle is 4cm less than the area of the square. If length of the rectangle is 14cm.

$\bf{\Large{\underline{\bf{To\:Find\::}}}}$

Perimeter of rectangle.

$\bf{\Large{\underline{\tt{\pink{Explanation\::}}}}}$

$\blacksquare$ We know that formula of the perimeter of a Square:

$\bf{\Large{\boxed{\sf{Perimeter\:Of\:square\:=\:4*side}}}}}}$

$\implies\sf{Perimeter\:=\:4*side}\\\\\\\\\implies\sf{48\:=\:4*side}\\\\\\\\\implies\sf{Side\:=\:\cancel{\dfrac{48}{4}} }\\\\\\\\\implies\sf{\purple{Side\:=\:12cm}}$

A/q

$\boxed{\begin{minipage}{6cm}\sf{Area\:of\:rectangle\:=\:Length*Breadth}\\ \\\sf{Area\:of\:Square\:=\:Side*Side}\end{minipage}}$

$\longmapsto\sf{Length*Breadth\:=\:(Side)^{2} -4cm}\\\\\\\\\longmapsto\sf{14cm*Breadth\:=\:(12cm)^{2} -4cm}\\\\\\\\\longmapsto\sf{14*Breadth\:=\:144cm-4cm}\\\\\\\\\longmapsto\sf{14*Breadth\:=\:140}\\\\\\\\\longmapsto\sf{Breadth\:=\:\cancel{\dfrac{140}{14} cm}}\\\\\\\\\longmapsto\sf{\purple{Breadth\:=\:10cm}}$

Now,

$\bf{\Large{\underline{\sf{\orange{\bigstar{Perimeter\:of\:Rectangle\::}}}}}}$

$\leadsto\sf{Perimeter\:=\:2(Length+Breadth)}\\\\\\\leadsto\sf{Perimeter\:=\:2(14cm+10cm)}\\\\\\\\\leadsto\sf{Perimeter\:=\:2(24cm)}\\\\\\\leadsto\sf{\purple{Perimeter\:=\:48cm}}$

Thus,

Perimeter is 48cm.