The diagonal of a rectangular field is 15 m and its length is 3 m more than its breadth.Find out the required quadratic equation in one variable

Explanation

Let the breadth of the field be x m.
`:.` length =(x+3)m
`:.` length of the diagonal `=sqrt(x^(2)+(x+3)^(2)m)` (as per fomaula
As per question, `=sqrt(x^(2)+(x+3)^(2))=15`
or, `x^(2)+(x+3)^(2)=(15)^(2)` (Squaring both the sides)
or, `x^(2)+x^(2)+6x+9=225`
or, `2x^(2)+6x+9-225=0`
or, `2x^(2)+6x+9-255=0`
or, `2x^(2)+6x-216=0`
or, `x^(2)+3x-108=0`
Hence the required quadratic equation in one variable is `x^(2)+3x-108=0`.