SOLUTION: Solve. The length of a rectangle is 1 cm longer than it's width. If the diagonal of the rectangle is 4 cm, what are the dimensions (length and width) of the rectangle?

Algebra ->  Rectangles -> SOLUTION: Solve. The length of a rectangle is 1 cm longer than it's width. If the diagonal of the rectangle is 4 cm, what are the dimensions (length and width) of the rectangle?      Log On


   



Question 122745: Solve.
The length of a rectangle is 1 cm longer than it's width. If the diagonal of the rectangle is 4 cm, what are the dimensions (length and width) of the rectangle?

Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

The length L of a rectangle is 1+cm longer than it's width W
=>…..L+=+W+%2B+1cm
the diagonal d of the rectangle is 4+cm
find: L and W
use Pythagorean Theorem
d%5E2+=+L%5E2+%2B+W%5E2
%284+cm+%29%5E2+=+%28W+%2B+1cm+%29%5E2+%2B+W%5E2
%284+cm+%29%5E2+=+W%5E2+%2B+2W+%2B+1cm%5E2+%2B+W%5E2
16cm%5E2+=+2W%5E2+%2B+2W+%2B+1cm%5E2+
+2W%5E2+%2B+2W+%2B+1cm%5E2+-+16cm%5E2+=+0+
+2W%5E2+%2B+2W+-+15cm%5E2+=+0+
+W+%5B1%2C2%5D=%28-2+%2B-+sqrt+%282%5E2+-4%2A2%2A%28-+15%29+%29%29+%2F+%282%2A2%29
+W+%5B1%2C2%5D=%28-2+%2B-+sqrt+%284+%2B+120+%29%29+%2F+4
+W+%5B1%2C2%5D=%28-2+%2B-+sqrt+%28124+%29%29+%2F+4
+W+%5B1%2C2%5D=%28-2+%2B-+11.14%29+%2F+4………you need only positive root
+W+%5B1%5D=%28-2+%2B+11.14%29+%2F+4
+W+%5B1%5D=+9.14+%2F+4
+W+%5B1%5D=+2.285
+W+%5B1%5D=+2.28cm
=>…..L+=+W+%2B+1cm
=>…..L+=+3.28cm

Check:
%284+cm+%29%5E2+=+%283.28cm%29%5E2+%2B+%282.28cm%29%5E2
16cm%5E2+=+10.75cm%5E2+%2B+5.19cm%5E2
16cm%5E2+=+15.94+cm%5E2
16cm%5E2+=+16+cm%5E2