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Word problems on Quadratic Equations (1)

Question:

The length of a back yard is 4 m. more than the breadth , area of the back yard is 320 `m^2`. Find the length and breadth of the yard.

Solution:

Let the breadth = `x`
Therefore the length = `4 + x`
Given that the area of yard is 320 `m^2`
So,
`x \cdot  ( x + 4) = 320`
`x^2 + 4x = 320`
`x^2 + 4x - 320 = 0` (Equation in the standard form)
`x^2 + 20x - 16x - 320` (Splitting the middle term)
`x(x + 20) -16(x + 20) = 0` (Factoring out x + 20)
`(x + 20) (x - 16) = 0`
`x + 20 = 0 x -16 = 0`
`x = -20, x = 16`

Answer

`x = 16` is the breadth
`4 + 16 = 20` is the length of the yard

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