Question

The area of a square field is 5184 m². A rectangular field, whose length is twice its
breadth, has its perimeter equal to the perimeter of the square field. Find the area
of the rectangular field.​

Answer 1

Step-by-step explanation:

a^2=5184

a=√5184

a=72

l=2b

2(l+b)=4a

2(2b+b)=4×72

3b=4×72÷2

3b=144

b=48

l=2×48=96

area of rectangular field= 96×48=4608

Answer 2

ATQ,

Perimeter of the square field = perimeter of the rectangular field

Given area of the square field = 5184m²

We know that,

Side² = area of a square

➡ side² = 5184m²

➡ side = √5184

➡ side = 72m

Thus it's perimeter = 4 × side (since a square has 4 equal sides)

= 4 × 72

= 288m

Therefore the perimeter of the rectangle is also 288m.

Now it's given that the length of the rectangular field is twice it's breadth.

Let the breadth of the rectangular field be x.

Therefore it's length = 2x

➡ 2 ( length + breadth ) = 288m

➡ 2(2x + x) = 288m

➡ 6x = 288m

➡ x = 288/6

➡ x = 48m

The dimensions of the rectangular field are :-

• breadth = x = 48m

• length = 2x = 96m

Hence, it's area = length × breadth

= 48 × 96

= 4608m² Final answer