Question

A 164 cm long rod is to be bend to make a rectangle. Its length should be 2 cm more than three times its breadth.

a). What should be the perimeter of the rectangle?

b). what should be the length and the breadth? ​

Answer 1

Given,

• The length of rod is 164 cm, which is to be trasformed as rectangle.

Also,

The length of newly formed rectangle should be :

• 2 cm more than thrice its width

So,

• Let the breadth of rectangle be b.

Then, Length of rectangle will be 3b + 2.

Here,

• Perimeter of rectangle should be same as the measure of length of rod.

$\because \: \: \textsf{The extend of rod has been rebent as}\\ \textsf{\: \: \: \: four - sided rectangle.}$

Thus,

$\small \bullet \: \text{Perimeter of newly created rectangle} = \rm{ \green{164} \: \blue{ cm}}$

Now,

• We need to obtain the dimensions of rectangle.

• For this purpose, we gotta equate the Actual Perimeter of rectangle(i.e. 164 cm) with Formulae of Perimeter of rectangle (i.e. 2[Length + Breadth])

We knew,

$\bullet \: \textbf{ \purple{Formulae of Permimeter of rectangle}} \\ \: \: \: \: \: \: \: \sf \longmapsto \orange{2(Length + Breadth )}$

Therefore,

$\to \: \rm{}2(Length + Breadth) = 164 \: cm$

¤ Dividing both sides by 2

$\to \rm{ \frac{ \cancel2(Length + Breadth)}{\cancel2} } = \frac{164}{2} = 82 \\ \\ \to \rm{Length + Breadth} = 82 \: cm$

¤ Putting the values of Length & Breadth, in obtained expression,

$\to \rm{(3b + 2)+b } = 82 \\ \to \rm{ \: \: \: \: \: \: \: 4b + 2} = 82$

¤ Subtracting 2 from both sides,

$\to \rm{4b + \cancel2 - \cancel2} = 82 - 2 \\ \to \rm{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 4b} = 80$

¤ Dividing both sides by 4,

$\to \rm{ \: \: \: \: \: \: \: \: \: \: \: \: \frac{ \cancel4b}{ \cancel4} } = \frac{80}{4} = 20 \\ \\ \to \rm{\: \: \: \: \: \: \: \: \: \: \: \:b = \red{ 20 \: cm}}$

We know,

• Length of rectangle = 3b + 2

So,

$\bf{}Length = 3 \times (20) + 2 \\ \bf\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 60 + 2 = \red{62} \: cm$

Hence,

• Breadth of rectangle is 20 cm

• Length of rectangle is 62 cm

Answer 2

Answer:

Breadth of rectangle is 20 cm

Length of rectangle is 62 cm

Step-by-step explanation: