Question

the length of a rectangle is 8m more than its breadth if its perimeter is 128m, find its length , breadth ​and Area​

Answer 1

Question:-

the length of a rectangle is 8m more than its breadth if its perimeter is 128m, find its length , breadth and Area

Answer:-

• The length of Rectangle is 36 m
• The breadth of rectangle is 28 m
• The area of Given rectangle is 1008 m².

To find:-

• Length and breadth of rectangle
• Area of rectangle

Solution:-

• Let the breadth be x
• Length = 8 + x
• Perimeter = 128 m

$\boxed{ \large{ \mathfrak{perimeter = 2(l + b)}}}$

According to question,

$\large{ \tt: \implies \: \: \: \: \: 2(8 + x + x) = 128}$

$\large{ \tt: \implies \: \: \: \: \: 8 + 2x = \frac{128}{2} }$

$\large{ \tt: \implies \: \: \: \: \: 8 + 2x = 64}$

$\large{ \tt: \implies \: \: \: \: \: 2x = 64 - 8}$

$\large{ \tt: \implies \: \: \: \: \: 2x = 56}$

$\large{ \tt: \implies \: \: \: \: \: x = 28}$

• The breadth of rectangle is 28 m
• Length = 8 + x = 28 + 8 = 36 m

$\large{ \boxed{ \mathfrak{area = l \times b}}}$

$\large{ \tt: \implies \: \: \: \: \: area = 28 \times 36}$

$\large{ \tt: \implies \: \: \: \: \: area = 1008 \: {m}^{2} }$

• The area of Given rectangle is 1008 m².

Answer 2

Diagram:

⇑ Attached picture :)

Question:

The length of a rectangle is 8m more than its breadth if its perimeter is 128m, find its length , breadth and Area

Explanation:

So first it is asked to find length and breadth. For this first we have to suppose breadth as x and length as x+8 . Then we have to use Perimeter of rectangle i.e. P=2(l+b) . By using this formula we can find value of x. By which we can find value of length and breadth. And then we can find Area by using this formula:Area=l×B

To find:

• Length
• Breadth
• Area

Given:

• Length of rectangle is 8 m more than breadth
• Perimeter = 128 m

Let:

• Breadth = x
• Length = 8+x

Formula Used:

• $\green {\sf{Perimeter \: of \: rectangle = 2(length + breadth)}}$
• $\green {\sf Area = length \times breadth}$

Answer:

We know :

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

$\therefore \sf 128 = 2(x + 8 + x)$

$\sf : \implies x + 8 + x = \dfrac{128}{2}$

$\sf : \implies x + 8 + x = \dfrac{ { \cancel{128}}^{ \: \: 64} }{ { \cancel{2}}^{ \: 1} }$

$: \implies \sf 2x + 8 = 64$

$\sf : \implies 2x = 64 - 8$

$\sf : \implies 2x = 56$

$: \implies \sf x = \dfrac{56}{2}$

$: \implies \sf x = \dfrac{ { \cancel{56}}^{ \: 28} }{ { \cancel{2}}^{ \: 1} }$

$: \implies \star \boxed{ \sf x = 28} \star$

As we have supposed Breadth

$\pink{ \therefore \boxed{ \sf Breadth = 28 \: cm}}$

As we have supposed Length=x+3

$\therefore \sf Length = 28 + 3$

$:\implies \pink{ \boxed{ \sf Length =36 \: cm}}$

Now Let's find Area of rectangle

We know

$\sf Area = length \times breadth$

$:\implies \sf Area = 28 \: cm \times 36 \: cm$

$:\implies \pink{ \boxed{\sf Area = 1008 \: {cm}^{2} }}$

$\underline {–———–—————–—————————–———————————————}$

And all we are done! ✔

:D