Question

A rectangular garden has an area of 245m2. If length is decreased by 14m and breadth is increased by 14m, then that become a square. Evaluate the perimeter of the rectangle (in m).

Answer 1

Answer:

Let the length and breadth of a rectangular garden be 5a m and 4a m respectively.

∴5a×4a=2000⟹a

2

=100⟹a=10

Hence, length of the garden =5×10=50m

and Breadth of the garden =4×10=40m

Let the uniform width of the road = x$$ m

∴ As per question,

50×40−[(50−2x)×(40−2x)]=344

⟹2000−2000+2x(50−40)−4x

2

=344

⟹4x

2

−180x+344=0

⟹x

2

−45x+86=0

⟹x

2

−43x−2x+86=0

⟹x(x−43)−2(x−43)=0

⟹(x−43)(x−2)=0

∴x=2m

Answer 2

Answer :-

Let Length of the rectangular garden is L m and Breadth is B m .

so,

→ Area of rectangular garden = L * B = LB = 245 m² -------- Eqn.(1)

now, given that, length is decreased by 14m and breadth is increased by 14m it becomes a square .

then,

→ L - 14 = B + 14

→ L - B = 28

→ L = (28 + B)

putting value of L in Eqn.(1),

→ (28 + B) * B = 245

→ B² + 28B - 245 = 0

→ B² + 35B - 7B - 245 = 0

→ B(B + 35) - 7(B + 35) = 0

→ (B + 35)(B - 7) = 0

→ B = (-35) or 7 . { since negative value of Breadth is not possible. }

therefore,

→ B = 7 m.

→ L = 28 + B = 35m .

hence,

→ Perimeter of rectangular garden = 2(L + B) = 2(35 + 7) = 2 * 42 = 84 m . (Ans.)