The perimeter of a rectangle is 42 cm A diagonal of the rectangle is 3 cm less than twice its - Maths - Second Degree Equations

Question

The perimeter of a rectangle is 42 cm A diagonal of the
rectangle is 3 cm less than twice its width let the width be x Then
find the length and diagonal in x Frame a second degree equation
based on the facts Find the length of the rectangle and
diagonal

Rishabh Mittal · Accepted Answer

Let the width be x cm
Diagonal will be 2x-3 cm
length=2x-32-x2=4x2+9-12x-x2=3x2+9-12xPerimeter=2length +width42=2 3x2+9-12x+x42-2x=23x2+9-12x21-x=3x2+9-12xSquaring on both sides , we get21-x2=3x2+9-12x2441-42x+x2=3x2+9-12x2x2+30x-432=0x2+15x-216=0x=-15±225-4-2162=-15±225+8642=-15±10892=-15±332=-482 and 182=-24 and 9 cm
width cant be negative 
 So, x=9 cm
And length=392+9-129=243+9-108=144=12 cm
Diagonal=29-3=15 cm

The perimeter of a rectangle is 42 cm.A diagonal of the rectangle is 3 cm less than twice its width.let the width be x.Then find the length and diagonal in x.Frame a second degree equation based on the facts. Find the length of the rectangle and diagonal.