Question

The length of a rectangle is increased by 10%. The breadth of the rectangle is increased by 20%. The perimeter of the rectangle increased by x%. The range of

Answer 1

Answer:

The value of x is 16.67

Step-by-step explanation:

The correct question is-"The length of a rectangle is increased by 10%. The breadth of the rectangle is increased by 20%. The perimeter of the rectangle increased by x%. Then the value of x is?"

Let the length of the rectangle be 100m and

The breadth of the rectangle be 200m.

The perimeter of rectangle is twice the sum of its length and breadth.

Therefore,we write $P=2(l+b)= > P=2(100+200)=600m$

According to the given data we can write

$\frac{\triangle l}{l} \times100=10= > l`=110m\\\frac{\triangle b}{b} \times100=20= > b`=240m$

Also given that,

The perimeter of the triangle is increased by x %.It is written mathematically as shown below

$\frac{\triangle P}{P} \times100=x= > \frac{P`-600}{600} \times100=x$

The increased perimeter is $P`=2(110+240)=700m$

Substituting this value in above relation we get,

$x=\frac{700-600}{600} \times 100=16.67\%$

Therefore,

The value of x is 16.67

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Answer 2

Complete Question: The length of $a$ rectangle is increased by $10$%. The breadth of $a$ rectangle is increased by $10$%. The perimeter of $a$ rectangle increased by $x$%. The value of x is

Answer:

The value of x is 10.

Step-by-step explanation:

Step 1 of 3

Let the length of a rectangle be $l$.

And the breadth of a rectangle be $b$.

Then,

The perimeter of a rectangle = 2($l+b$)

⇒ P = 2($l+b$) . . . . . (i)

Step 2 of 3

The length of $a$ rectangle is increased by 10%, i.e.,

So, the new length of a rectangle is,

$l'$ = $l$ + 10% of $l$

  = $l+\frac{l}{10}$

  = $\frac{11l}{10}$

The breadth of $a$ rectangle is increased by 10%, i.e.,

So, the new length of a rectangle is,

$b'$ = $b$ + 10% of $b$

  = $b+\frac{b}{10}$

  = $\frac{11b}{10}$

The new perimeter of a rectangle is,

P' = 2$\left(\frac{11l}{10}+\frac{11b}{10} \right)$

   = $2\left(\frac{11l+12b}{10} \right)$

   = $\frac{11}{5}(l+b)$

Step 3 of 3

Increase in perimeter = New perimeter - the original perimeter

                                    = $\frac{11}{5}(l+b)-2(l+b)$

                                    = $\frac{11(l+b)-10(l+b)}{5}$

                                    = $\frac{l+b}{5}$

The percentage increase in perimeter = $\frac{Increase\ in\ perimeter}{The \ original\ perimeter} \times 100$

⇒ x% = $\frac{(l+b)/5 }{2(l+b)}\times 100$

⇒ x% = $\frac{1}{10}\times 100$

⇒ x% = 10%

Therefore, the value of x is 10.

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