SOLUTION: the diagonal of a rectangle is 2 centimeters longer than its length and 9 centimeters greater than its width. find the dimensions of the rectangle.

Question 684555: the diagonal of a rectangle is 2 centimeters longer than its length and 9 centimeters greater than its width. find the dimensions of the rectangle.
Answer by Jolliano(16) (Show Source): You can put this solution on YOUR website!
Let d be length of diagonal,h be height and w be width.
The length,width and diagonal form a right angled triangle with the diagonal as the hypotenuse.
From the question,
d = h + 2 .........(1) and
d = w + 9 ........(2).
Equating both,
h + 2 = w + 9
h = w + 9 - 2
h = w +7..............(3)
Using Pythagoras theorem,
h^2 + w^2 = d^2
Sub h with (3) and d with (2)
(w + 7)^2 + w^2 = (w + 9)^2
w^2 + 14w + 49 + w^2 = w^2 +18w + 81
Collecting like terms,
w^2 - 4w - 32= 0
Factorizing,
(w + 4)(w - 8) = 0
w = -4 or 8.
The Width cannot be negative so
Width = 8cm
From (3)
h = w + 7 = 8 + 7 = 15cm.
From (2)
d = w + 9 = 8 + 9 = 17cm.
RELATED QUESTIONS
the diagonal of a rectangle is 2cm longer than its length and 9cm greater than its width. (answered by ewatrrr)

A rectangle has a diagonal that measures 10 centimeters and a length that is 2... (answered by checkley77)

The length of a rectangle is 4 centimeters longer than its width. If the perimeter is 28... (answered by dabanfield)

The length of a rectangle is 4 centimeters longer than its width. The area of the... (answered by Boreal)

What is the the length and width of a rectangle if the length is 4 centimeters longer... (answered by askmemath)

the length of a rectangle is 8 centimeters greater than its width. Find the dimensions of (answered by jojo14344)

A rectangle has a diagonal that measures 10 centimeters and lengh that is 2 centimeters... (answered by orca)

The length of a certain rectangle is 4 centimeters longer than its width. And the number... (answered by ankor@dixie-net.com)