A rectangular field is 16 m longer than it is wide and has an area of 192 sq m. If the field's width is x metres, then x(x + 16) = 192, which gives the equation x^2 + 16x - 192 = 0. Find the width x of the field.

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Accepted Answer

8. x^2 + 16x - 192 = 0 factors as (x - 8)(x + 24) = 0, giving x = 8 or x = -24. Width is positive, so x = 8 m (length 24 m, area 8 x 24 = 192).

A rectangular field is 16 m longer than it is wide and has an area of 192 sq m. If the field's width is $x$ metres, then $x (x + 16) = 192$ , which gives the equation $x^{2} + 16 x - 192 = 0$ .
Find the width $x$ of the field.

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More Class 10 Standard Form and Roots practice

A rectangular field is 16 m longer than it is wide and has an area of 192 sq m. If the field's width is x metres, then x(x+16)=192, which gives the equation x2+16x−192=0.Find the width x of the field.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Standard Form and Roots practice

A rectangular field is 16 m longer than it is wide and has an area of 192 sq m. If the field's width is $x$ metres, then $x (x + 16) = 192$ , which gives the equation $x^{2} + 16 x - 192 = 0$ .
Find the width $x$ of the field.