Question

the length of the rectangle is 3cm more than its breadth its perimetre is 34cm. find
the length and breadth
​

Answer 1

• Length of rectangle is 10 cm.
• Breadth of rectangle is 7 cm.

Step-by-step explanation:

Given :-

• Length of rectangle is 3 cm more than its breadth.
• Perimeter of rectangle is 34 cm.

To find:-

• Length and Breadth of rectangle.

Solution:-

Let, Breadth of rectangle be x.

And Length be x + 3 [We have taken Length be x + 3 because it given that, length of rectangle is 3 cm more than its Breadth]

Perimeter of rectangle = 2(l + b)

• Here, l and b are length and breadth of rectangle.

Put, Length, breadth and perimeter of rectangle in formula :

$\longrightarrow$ 34 = 2(x + 3 + x)

$\longrightarrow$ 34 = 2x + 6 + 2x

$\longrightarrow$ 34 = 4x + 6

$\longrightarrow$ 34 - 6 = 4x

$\longrightarrow$ 28 = 4x

$\longrightarrow$ 28/4 = x

$\longrightarrow$ 7 = x

Or, $\longrightarrow$ x = 7

Verification:-

$\longrightarrow$ 34 = 2(x + 3 + x)

• Put x = 7

$\longrightarrow$ 34 = 2(7 + 3 + 7)

$\longrightarrow$ 34 = 2(10 + 7)

$\longrightarrow$ 34 = 20 + 14

$\longrightarrow$ 34 = 34

Hence, Verified!!

We have taken, Breadth be x. So, Breadth of rectangle is 7 cm.

We have also taken, Length be x + 3 = 7 + 3 = 10. Thus, Length of rectangle is 10 cm.

Answer 2

Answer:

$\huge \boxed { \bf let}$

• Breadth of rectangle = x
• Length of rectangle = x +3

$\sf therefore$

$\sf \: 34 = 2(x + 3 + x)$

Now,

$\huge \bf \: P\: = 2(L + B)$

$\sf \implies \:34 = 2(x + 3 + x)$

$\sf \implies \: 34 = 2x + 2x + 6$

$\sf \implies \: 34 = 4x + 6$

$\sf \implies \: 4x = 34 - 6$

$\sf \implies4x = 28$

$\sf \implies \: x = \dfrac{28}{4}$

$\huge \fbox { x \: = 7}$

• Breadth (B) = 7 .
• Length (L) = 7 + 3 = 10 cm .

Let's verify

$\bf \: 34 = 2(x + 3 + x)$

$\bf \: 34 = 2(7 + 3 + 7)$

$\bf \: 34 = 2(17)$

$\bf \: 34 = 34$