A room is 4 feet longer than its width. If the diagonal of the room is 20 feet. What is its length and width

Question

Let x be the width

let x+4 be the length 

diagonal of room is 20 feet

Answer 1

Your problem should really state the room is rectangular. That way, you may realize that when you draw the diagonal, you get 2 congruent right triangles and can use the Pythagorean Theorem. So your 2 legs would be x and x+4 and the hypotenuse would be 20.

 

So x² + (x+4)² = 20²

    x²  + (x+4)(x+4) = 400    use FOIL

    x² + x² +4x+4x+16 = 400     combine like terms

   2x² + 8x + 16 = 400       since all terms are even, divide everything by 2 to make factoring easier

   x² + 4x + 8 = 200          gather everything on one side and 0 on the other before you factor

   x² + 4x - 192 = 0           numbers must multiply to -192 and add to 4

  (x+16)(x-12) = 0

 

x+16=0 or x-12 =0

So x=-16 or x=12.

 

Since lengths cannot be negative, -16 is rejected and x= 12 is your width making 16 your length.

 

Hope this helped.