Question

${\orange{\bigstar}}\{\underline{\red{\textsf{\textsf{Question:-}}}}$

A square field is made bigger by adding 5m to the length and 2m to the width. The area of the new (bigger) field is 130cm^2.
Find the length of a side of original field.​

Answer 1

Correct question:

• A square field is made bigger by adding 5m to length and 2m to width. The area of new field is $\small{\underline{\bf{\orange{130m^2}}}}$ Find the length of a side of original field.

Given:

• A square field is made bigger by adding 5m to the length and 2m to the width.
• Area of new field is 130m²

To Find:

• Side of original side?

Solution:

We have given that orginal field is in shape of square and in that square, we added 5m in length and 2m in width. Now, new field will be in shape of rectangle.

■ Let suppose that original field was with side of x

Therefore,

• Length of new field = x + 5
• width of new field = x + 2

We know that :

• $\large{\boxed{\bf{\green{Area~of~rectangle~=~length\times width}}}}$

Where,

• Area of rectangle = 130
• length of rectangle = x + 5
• breadth of rectangle = x + 2

Let put values in formula :-

Area of rectangle = length × width

→ 130 = (x + 5)(x+2)

→ 130 = x(x + 2) +5(x + 2)

→ 130 = x² + 2x + 5x + 10

→ 130 = x² + 7x + 10

→ x² + 7x + 10 - 130 = 0

→ x² + 7x - 120 = 0

Factorising :-

x² + 7x - 120 = 0

→ x² + 15x - 8x - 120 = 0

→ x(x + 15) - 8(x + 15) = 0

→ (x - 8) (x + 15)

→ x = 8 or x = -15

So, we can say that side of square (original field) will be 8m or -15m.

But, length of anything can't be in -ve

Therefore,

• $\large{\boxed{\pink{\bf{Side~of~original~field~is~8m}}}}$

Answer 2

$\begin{gathered}\large {\boxed{\sf{\mid{\overline {\underline {\star ANSWER ::}}}\mid}}}\end{gathered}$

Given :-

➪ A square field is made bigger by adding 5m to the length and 2m to the width.

➪ The area of the new (bigger) field is 130cm^2.

To Find :-

➪ Length of a side of original field.

Solution :-

To be noted that :

$\large \boxed{All \: sides \: of \: a \: square \: are \: equal}$

Let the sides of the initial square be 'x meters'

So, the sides of the new rectangular field formed is :

• length = x + 5 m
• breadth = x + 2 m

Also, Area of the new rectangular field = length x breadth

Area of the new rectangular field = (x + 5)(x + 2)

Given, Area = 130 m^2

therefore, (x + 5)(x + 2) = 130

${x}^{2} + 2x + 5x + 10 = 130 \\ {x}^{2} + 7x + 10 = 130 \\ {x}^{2} + 7x - 120 = 0$

By solving further,

• x = -15 and 8

As length can't be negative,

$\large \boxed{side \: of \: original \: field \: = 8}$

@SweetestBitter