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

Answer:

Let breadth of the rectangle is x.

Then its length will be 2x−16.

According to the problem,

2(length+breadth)=100

2(x+2x−16)=100

or, 6x=132

or, x=22.

Then length is

=2x−16

=44−16=28 cm.

Answer 2

Question:-

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:-

• Length of the rectangle is 28 cm
• Breadth of the rectangle is 22 cm

Explanation:-

Given:-

• Length of a rectangle is 16 cm less than twice its breadth

• perimeter of the rectangle is 100 cm

To find:-

• Length of the rectangle

• Breadth of the rectangle

Solution:-

Let, the breadth of the rectangle is x cm

then, length is (2x - 16) cm

We know that,

${\underline{\boxed{\sf{Perimeter\:of\:rectangle=2(Length+Breadth)}}}}$

According to the question,

➥ 2(2x - 16 + x) = 100

➥ 2(3x - 16) = 100

➥ (3x - 16) = 50

➥ 3x - 16 = 50

➥ 3x = 50 + 16

➥ 3x = 66

➥ x = 22

Therefore,

• Breadth of the rectangle is 22 cm

• Length of the rectangle is (2×22-16) = 28 cm

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❑ Formulas of Rectangle:-

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

1. Area of rectangle = Length × Breadth

2. Perimeter of rectangle = 2(Length + Breadth)

3. Diagonal of rectangle= ${\sf \sqrt{(length)^{2}+(breadth) ^{2}}}$

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