Question

3. The length and the breadth of a rectangular field are in the ratio 5:3. If its perimeter is
128 m, find the dimensions of the field.​

Answer 1

Question:-

The length and the breadth of a rectangular field are in the ratio 5:3. If its perimeter is 128 m, find the dimensions of the field.

Answer:-

• The length and breadth of rectangle are 40 m and 24 m

To find:-

• Length and breadth of rectangle

Solution:-

• Ratio = 5:3
• Perimeter of rectangle = 128 m

Let,

• Length of rectangle = 5x
• Breadth of rectangle = 3x

As we know,

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

Where,

• l = length of rectangle
• b = breadth of rectangle

According to question,

$\Large{\sf: \implies \: \: \: \: \: \: \: \: 2(5x + 3x) = 128}$

$\Large{\sf: \implies \: \: \: \: \: \: \: \: 8x = \frac{128}{2} }$

$\Large{\sf: \implies \: \: \: \: \: \: \: \: 8x = 64}$

$\Large{\sf: \implies \: \: \: \: \: \: \: \: x = \frac{64}{8} }$

$\Large{\sf: \implies \: \: \: \: \: \: \: \: x = 8}$

Now,

• length of rectangle = 5x = 40 m
• Breadth of rectangle = 3x = 24 m

Hence,

The length and breadth of rectangle are 40 m and 24 m

Answer 2

Step-by-step explanation:

perimeter of field =128m

l/b=5:3

l=5b/3..........(1)

perimeter of field =2(l+b)

128=2(5b/3 + b)

64= (5b+3b)/3

192=8b

b=24m

put value of b in eq. (1),

l=5×24/3

l= 40m