Question

The perimeter of rectangular field is 28 cm and its area is 48 cm². Find its length and
breadth.​

Answer 1

Given

Perimeter of Rectangular field is 28cm and it's area is 48cm².

To Find

We have to find its length and breadth

$\sf\huge {\underline{\underline{{Solution}}}}$

How to solve ?

step 1:Firstly we will apply perimeter or area formula of Rectangle and mark them Equation 1 and 2.

Step 2:From Equation 1 or 2 and we will convert the whole Equation either in the form of length or breadth and then substitute into another equation.

Step 3: We will find one value either l or b then again put into another Equation to find other value.

Since, perimeter of Rectangular field= 2(l+b)

Perimeter is 28cm

Our Equation becomes: 28= 2(l+b)----(1)

Area of Rectangular field= length * breadth

since ,area is 48cm²

Our Equation becomes: 48= l*b------(2)

From equation 1

=> 14 = l+b

l= 14-b----(3)

Substitute Equation 3 into 2

=> 48= (14-b)*b

=> 48= 14b-b²

=> 48-14b+b²

=> b²-14b+48

=> b²-8b-6b+48

=> b(b-8)-6(b-8)

=> (b-6)(b-8)

Makes equal to zero

we get b = 6 or b=8

Substitute b's value into equation 3

When b = 6

=>l= 14-6

length = 8

when b= 8

l= 14-8=6

Hence,length is 8cm or 6cm.

Breadth is 6cm or 8cm

Extra information=>

Area is Space or region which is covered by a solid object/figure it is said to be area of that object.

Area depends upon the dimensions of the figure.If dimensions is larger then larger will be the area of that object/figure and vice -versa.

Perimeter

Perimeter is the total distance occupy by a solid 2D figure around its edge.

Answer 2

Answer:

Answer :-

To find length and breadth of the rectangular field.

________________________________

Given,

perimeter = 28cm

and, area = 48cm²

________________________________

Perimeter of rectangle = 2(L+b)

=> 28cm = 2(L+b)

=> 14 cm = L +b

=> 14 - L = b...(I)

Now Area = L × b

=> 48cm² = L × b

here substitute the value of b and solve:-

=> 48cm² = L(14-L)

=> 48cm² = 14L - L²

=> L² -14L + 48 = 0

=> L² - 6L - 8L + 48 = 0

=> L( L - 6) - 8(L- 6) = 0

=> (L -8)(L-6) = 0

L = 8 or. L = 6

Now if L = 8

then b = 14 - L

=> 14 - 8

=> 6 cm

else L = 6

b = 14 - 6

=> 8 cm

________________________________

Hope it's helpful

Thank you