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

Step-by-step explanation:

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,

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

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

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

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

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

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

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

Given:

l = b + 8  ..................................(i)

perimeter = 128m

to find:

l , b and area

Basic Approach

getting the value of l and b and then calculating area

Solution:

perimeter of rectangle = 2(l+b)

128 = 2(l +b)

now, by (i) we get:-

128 = 2(b + b +8)

4b + 16 = 128

4b = 128 - 16

4b = 112

b = 28 m

now  , l = b +8

l = 28 + 8

l  = 36 m

Now, area of rectangle  = lb

= 28 * 36 cm^2

= 1008 m^2

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