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

Answer:

8 cm

Step-by-step explanation:

Given:

• A square field is made bigger by adding 5 m to the length and 2 m to the width.
• The area of the new (bigger) field is 130 cm².

To find:

• The length of a side of original field.

Solution:

Let the length of a side of original square field be x.

Then,

Square field is made bigger.

• Length of new ( bigger ) field = ( x + 5 ) m
• Breadth of new ( bigger ) field = ( x + 2 ) m

✰ Area = l × b

Here,

l is the length of new ( bigger ) field.

b is the breadth of new ( bigger ) field.

Putting the values in the formula, we have:

• 130 = ( x + 5 ) × ( x + 2 )
• 130 = x( x + 2 ) +5( x + 2 )
• 130 = x² + 2x + 5x + 10
• 130 = x² + 7x + 10
• 130 - 10 = x² + 7x
• 120 = x² + 7x
• x² + 7x - 120 = 0
• x² + 15x - 8x - 120 = 0
• x(x + 15) - 8(x + 15) = 0
• ( x - 8 ) ( x + 15 ) = 0

Take,

• x - 8 = 0
• x = 8

Now, take

• x + 15 = 0
• x = - 15

Length of side of square can't be negative, therefore the length of a side of original field = 8 m

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