Question

A rectangle with perimeter 220cm is divided into five congruent rectangle as shown in the diagram.what is the perimeter of one of the five congruent rectangle

Answer 1

Thus, Perimeter of one of the five congruent rectangle is $100cm$

Step-by-step explanation:

A rectangle with perimeter $220cm$ is divided into five congruent as shown in the figure.

From perimeter of rectangle,

∴$2(A+B)=220$

⇒$(A+B)=110$

In figure,

$A=b+b+b=3b$

Also, $A=a+a=2a$ and

$B=a+b$

∵$(A+B)=110$

⇒$(2a+a+b)=110$

⇒$3a+b=110$ __$1$

Also,

⇒$3b+a+b=110$

⇒$a+4b=110$__$2$

By multiplying $3$ with equation-$2$ and subtract with equation-$1$,

  $3a+12b-3a-b=330-110$

⇒$11b=220$

⇒$b=20$

Plug $b$ value in equation-$2$,

$a+(4\times 20)=110$

⇒$a=110-80$

⇒$a=30$

∴ Perimeter of every small rectangle$=2(a+b)=2(20+30)=100cm$

So, Perimeter of one of the five congruent rectangle is $100cm$

Answer 2

The perimeter of the smaller rectangle is 100 cm.

Refer to the figure attached.

Let the length of the congruent rectangles be 'x' and the breadth be 'y'.

Now, given that the perimeter of the bigger rectangle is 220 cm.

So, sum of all sides of the bigger rectangle is 220 cm.

So, AB+BC+CD+AD= 220

(y+y+y)+(x+y)+(x+x)+(x+y)= 220

4x+5y= 220 ------------------ [I]

Now, in a rectangle, opposite sides are equal.

So, AB= CD

y+y+y = x+x

3y= 2x --------------- [II]

6y= 4x --------------- [III]

Substituting [III] in [I],

11y= 220

y= 20 ------------------ [III]

3y= 60 ------------------- [IV]

substituting [IV] in [II] we get,

60= 2x

x= 30 ----------------- [V]

Now, perimeter of the smaller rectangle = 2(x+y) ------------ [VI]

Substituting [III] and [V] in [VI] we get,

2 (30+20)

2×50 = 100 cm.