Question

Suppose you want to draw a rectangle where the width is 7 inches less than the length and the diagonal is 2 inches longer than the length. what are the dimensions of the rectangle?

Answer 1

The diagonal of a rectangle is:
 d ^ 2 = w ^ 2 + l ^ 2
 Where,
 w: width
 l: long
 Substituting values we have:
 (l + 2) ^ 2 = (l-7) ^ 2 + l ^ 2
 Rewriting we have:
 l ^ 2 + 4l + 4 = l ^ 2 -14l + 49 + l ^ 2
 l ^ 2 -14l + 49 - 4l - 4 = 0
 l ^ 2 -18l + 45 = 0
 (l-15) (l-3) = 0
 The solutions are:
 l = 15
 l = 3
 The viable solution is:
 l = 15
 Thus, the width is:
 w = l-7
 w = 15-7
 w = 8
 Answer:
 the dimensions of the rectangle are:
 l = 15
 w = 8