Question

When each side of a given square is increased by 4 feet the area is increased by 64 square feet. Deter mine the dimensions of the original square.

Answer 1

Answer:

so original square side was 6 cm

Answer 2

The length of each side of the square = 6 feet

Given :

When each side of a given square is increased by 4 feet the area is increased by 64 square feet

To find :

The length of each side of the square

Formula :

For square of side a unit

The area of the square = a² sq.unit

Solution :

Step 1 of 2 :

Form the equation to calculate length of each side of the square

Let length of each side of the square = x feet

∴ Area of the original square = x² square feet

When each side of a given square is increased by 4 feet then length of each side of the square becomes (x + 4) feet

Then area of the original square becomes (x + 4)² square feet

By the given condition

$\displaystyle \sf {(x + 4)}^{2} - {x}^{2} = 64$

Step 2 of 2 :

Calculate length of each side of the square

$\displaystyle \sf {(x + 4)}^{2} - {x}^{2} = 64$

$\displaystyle \sf{ \implies } ({x}^{2} + 2.x.4 + {4}^{2} ) - {x}^{2} = 64$

$\displaystyle \sf{ \implies } ({x}^{2} + 8x+ 16 ) - {x}^{2} = 64$

$\displaystyle \sf{ \implies } 8x + 16 = 64$

$\displaystyle \sf{ \implies } 8x = 64 - 16$

$\displaystyle \sf{ \implies } 8x = 48$

$\displaystyle \sf{ \implies }x = \frac{48}{8}$

$\displaystyle \sf{ \implies }x = 6$

Hence length of each side of the square = 6 feet

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