Question

the perimeter of a rectangle is 200 cm . it length is 3 time its breath. find his length and breath​

Answer 1

Step-by-step explanation:

200= 2x l+b

200=2xl+3

200= 2l +3

l=200/5

l= 40

I think

I didn't know exact solution

Answer 2

${\large{\pmb{\sf{\underline{Understanding \; the \; Question...}}}}}$

This question says that we have to find the actual length and breadth of a rectangle whose perimeter is given as 200 cm and also given that the length of this rectangle is 3 times it's breadth

Let us see that where is length and breadth of a rectangle located and let's see some definitions too -

Diagram is given below which show where is length and breadth located -

$\begin{gathered}\begin{gathered} \sf Length \: \: \: \: \: \: \: \: \: \: \: \\ \begin{gathered}\begin{gathered}\boxed{\begin{array}{}\bf {\red{}}\\{\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}\\ { \sf{ }}\\ { \sf{ }} \\ \\ { \sf{ }}\end{array}}\end{gathered}\end{gathered} \sf Breadth \end{gathered}\end{gathered}$

Some definitions are given below related to this question -

(1) Length: Length measures that how much long an object is to other points.

(2) Breadth: Breadth is the width of a shape.

(3) Perimeter: Perimeter is the distance along the lines forming a closed figure when we go round the figure ones. Means, perimeter is the length of the boundary of given closed figure.

(4) Rectangle: A rectangle is a two dimensional shape, it have 4 sides and 4 corners. It's two sides are equal to each other and the left two are equal to each other. Except of diagonal it have length and breadth.

${\large{\pmb{\sf{\underline{Given \; that...}}}}}$

• A rectangle is given.
• Perimeter = 200 cm.
• Length is 3 times it's breadth.

${\large{\pmb{\sf{\underline{To \; find...}}}}}$

• Length of rectangle.
• Breadth of rectangle.

${\large{\pmb{\sf{\underline{Solution...}}}}}$

• Length of rectangle = 75 cm
• Breadth of rectangle = 25 cm

${\large{\pmb{\sf{\underline{Using \; formulas...}}}}}$

${\small{\underline{\boxed{\sf{Perimeter \: of \: rectangle = 2(length+breadth)}}}}}$

${\small{\underline{\boxed{\sf{Area \: of \: rectangle = Length \times Breadth}}}}}$

${\large{\pmb{\sf{\underline{Assumptions...}}}}}$

As it's given that the length of this rectangle is 3 times it's breadth. Henceforth, we have to assume the length and breadth according to this.

• Length be 3a
• Breadth be a

The diagram of this question be as below -

$\begin{gathered}\begin{gathered} \sf 3a \: \: \: \: \: \: \: \: \: \: \: \\ \begin{gathered}\begin{gathered}\boxed{\begin{array}{}\bf {\red{}}\\{\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}\\ { \sf{ }}\\ { \sf{ }} \\ \\ { \sf{ }}\end{array}}\end{gathered}\end{gathered} \sf \: \: a\end{gathered}\end{gathered}$

${\large{\pmb{\sf{\underline{Full \; Solution...}}}}}$

~ To solve this question firstly we have to use the formula to find perimeter of rectangle then we have to put the values according to that formula! Then we get the value of a easily means breadth then we just have to substitute the value of a in 3a and we get the value of length too. Let's solve this question!

${\sf{:\implies Perimeter \: = 2(l+b)}}$

${\sf{:\implies 200 \: = 2(3a+a)}}$

${\sf{:\implies 200 \: = 2(3a+1a)}}$

${\sf{:\implies 200 \: = 2(4a)}}$

${\sf{:\implies 200 \: = 2 \times 4a}}$

${\sf{:\implies 200 \: = 8a}}$

${\sf{:\implies 200/8 = \: a}}$

${\sf{:\implies 100/4 = \: a}}$

${\sf{:\implies 50/2 =\: a}}$

${\sf{:\implies 25 = \: a}}$

${\sf{:\implies a = \: 25 \: cm}}$

${\sf{:\implies Breadth \: = 25 \: cm}}$

${\underline{\frak{Breadth \: of \: rectangle \: is \: 25 \: cm}}}$

~ Now finding length by using value of a there!

${\sf{:\implies Length \: = 3a}}$

${\sf{:\implies Length \: = 3(25)}}$

${\sf{:\implies Length \: = 3 \times 25}}$

${\sf{:\implies Length \: = 75 \: cm}}$

${\underline{\frak{Length \: of \: rectangle \: is \: 75 \: cm}}}$

Now the diagram of this question is looking like as given below -

$\begin{gathered}\begin{gathered} \sf 75 \: cm \: \: \: \: \: \: \: \: \: \: \: \\ \begin{gathered}\begin{gathered}\boxed{\begin{array}{}\bf {\red{}}\\{\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}\\ { \sf{ }}\\ { \sf{ }} \\ \\ { \sf{ }}\end{array}}\end{gathered}\end{gathered} \sf \: \: 25 \: cm \end{gathered}\end{gathered}$