Question

The dimensions of a rectangular garden were 3m by 10m. When both dimensions were increased by equal amounts, the area of the garden doubled. Find the dimensions of the new garden.

Answer 1

Dimensions of rectangular garden:

Length(l) = 10 m

Breadth(b) = 3 m

Area of rectangular garden = l * b

= 10 * 3

= 30 m^2

Let the dimensions be increased by X m

Then,

New Length(L) = ( 10 + X ) m

New Breadth(B) = (3 + X ) m

According to question, the area gets doubled :

New area = 2 * 30

L * B = 60 m^2

= (10 + X )(3 + X ) = 60

= 30 + 3x + 10x + x^2 = 60

= x^2 + 13x + 30 = 60

= x^2 + 13x + 30 - 60 = 0

= x^2 + 13x - 30 = 0

= x^2 + 15x - 2x - 30 = 0

= X(X + 15) - 2(X + 15) = 0

= (x - 2)(X + 15) = 0

= X - 2 = 0. X + 15 = 0

= X = 2 m. X = - 15.

Since, X = - 15 is not possible ( dimensions cannot be negative)

X = 2 m

New dimensions:

Length = 10 + X = 10+ 2 = 12 m

Breadth = 3 + X = 3 + 2 = 5 m

Answer 2

$\bf{\blue{\underline{\bf{Given}}}}$

The dimensions of a rectangular garden were 3 m by 10 m. When both dimensions were increased by equal amounts, the area of the garden doubled.

$\bf{\blue{\underline{\bf{To Find}}}}$

• Dimensions of new garden (Rectangle)

$\bf{\blue{\underline{\bf{Solution}}}}$

➤ ᴏʀɪɢɪɴᴀʟ ʀᴇᴄᴛᴀɴɢʟᴇ :-

• Length (l) = 10m

• Breadth (b) = 3m

➠ Area of Rectangle = l × b

➠ Area = 10×3 = 30 m²

➤ ɴᴇᴡ ʀᴇᴄᴛᴀɴɢʟᴇ :-

➦ Let the amount to be increased be 'x' m

Then,

➧ Area of New Rectangle = 2 × Area of Original Rectangle

➦ Area = 2 × 30 = 60m²

Now,

• Length (l) = ( 10 + x) m

• Breadth (b) = ( 3 + x) m

So,

➠ Area = l × b

↦ 60 = (10 + x) (3 + x)

↦ 60 = 30 + 10x + 3x + x²

↦ 60 = 30 + 13x + x²

↦ x² + 13x - 60 + 30 = 0

↦ x² + 13x - 30 = 0

↦ x² + 15x - 2x - 30 = 0

↦ x(x + 15) - 2(x + 15) = 0

↦ (x - 2)(x + 15) = 0

↦ x = 2. or x = -15

Hence,

➦ Length can't be negative.

So we take x = 2

Now,

• Length = ( 10 + x) = 10 + 2 = 12 m

• Breadth = ( 3 + x) = 3 + 2 = 5 m