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?

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