Question

The length of a rectangle is 16 cm more than its breadth. If the perimeter is 148 cm find the length and breadth of the rectangle.​

Answer 1

Given:

• Length of Rectangle is 16 cm more than its breadth.
• Perimeter of Rectangle = 148 cm

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To find:

• Length and breadth of Rectangle?

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Solution:

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☯ Let breadth of rectangle be x cm.

☯ Therefore, Length of rectangle (x + 16) cm.

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$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large (x + 16) cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large x cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

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$\underline{\bigstar\:\boldsymbol{According\: to\:the\:question\::}}$

$:\implies\sf 2(x + (x + 16)) = 148$

$:\implies\sf (x + (x + 16) = \cancel{\dfrac{148}{2}}$

$:\implies\sf (x + (x + 16) = 74$

$:\implies\sf 2x + 16 = 74$

$:\implies\sf 2x = 74 - 16$

$:\implies\sf 2x = 58$

$:\implies\sf x = \cancel{ \dfrac{58}{2}}$

$:\implies{\boxed{\sf{\pink{x = 29}}}}\;\bigstar$

Therefore,

• Breadth of Rectangle, x = 29 cm
• Length of Rectangle, (x + 16) = 45 cm

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∴ Hence, Length and Breadth of rectangle is 45 cm and 29 cm respectively.

Answer 2

Answer:

Given :-

• The length of a rectangle is 16 cm more than its breadth.
• Perimeter is 148 cm.

To Find:-

• What is the length and breadth of the rectangle.

Solution :-

Let, the breadth be x

And, the length of a rectangle is 16 cm more than its breadth then the length will be x + 16

According to the question,

⇒ 2(length + breadth) = 148

⇒ 2(x + x + 16) = 148

⇒ x + x + 16 = $\sf\dfrac{\cancel{148}}{\cancel{2}}$

⇒ x + x + 16 = 74

⇒ 2x + 16 = 74

⇒ 2x = 74 - 16

⇒ 2x = 58

⇒ x = $\sf\dfrac{\cancel{58}}{\cancel{2}}$

➠ x = 29 cm

Hence, the required length and breadth are,

✦ Breadth of a rectangle = x = 29 cm

✦ Length of a rectangle = x + 16 = 29 + 16 = 45 cm

$\therefore$ The length of a rectangle is 29 cm and the breadth of a rectangle is 45 cm .