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