Question

5. Is it possible to design a rectangular park of perimeter 80 m and area 400 mº? If so, find
its length and breadth.
​

Answer 1

Given

Is it possible to design a rectangular park of perimeter 80 m and area 400 m?

To find

Find the length and breadth

Solution

★ Let the length be " l " and breadth

be " b "

According to the given condition

★ Area of rectangular park = 400m²

→ length × breadth = 400

→ lb = 400 ----(i)

Now,

★ Perimeter of rectangular park = 80m

→ 2(length + breadth) = 80

→ l + b = 40

→ l = 40 - b ----(ii)

Putting the value of "l" in eqⁿ (i)

→ lb = 400

→ (40 - b)b = 400

→ 40b - b² = 400

→ b² - 40b + 400 = 0

Split middle term

→ b² - 20b - 20b + 400 = 0

→ b(b - 20) - 20(b - 20) = 0

→ (b - 20)(b - 20) = 0

So,

→ b - 20 = 0

→ b = 20 m

Putting the value of " b " in eqⁿ (ii)

→ l = 40 - b

→ l = 40 - 20

→ l = 20m

Hence,

Required length = 20m

Required breadth = 20m

Answer 2

ɢɪᴠᴇɴ :-

• Perimeter = 80 m

• Area = 400 m²

ᴛᴏ ғɪɴᴅ :-

• Length and Breadth if it is possible

sᴏʟᴜᴛɪᴏɴ :-

We know that,

➦ Perimeter of Rectangle = 2(l + b)

➭ 2( l + b) = 80

➭ ( l + b) = 80/2

➭ ( l + b) = 40

➭ l = ( 40 - b) --(1)

Now,

➦ Area of Rectangle = l × b

➭ ( l × b) = 400. --(2)

Substitute the value of (1) in (2) , we get,

➭ ( 40 - b) ×b = 400

➭ 40b - b² = 400

➭ b² - 40b + 400 = 0

➭ b² - 20b - 20b + 400 = 0

➭ b( b - 20) - 20( b - 20) = 0

➭ (b - 20) ( b - 20) = 0

➭ b = 20 or b = 20

Put b = 20 in (1) , we get

➭ l = (40 - b)

➭ l = (40 - 20)

➭ l = 20

Hence

• Length = Breadth = 20 m

So,

• Given condition is valid for Square not for Rectangle.