Answer:
The length is 12 cm, and the width is 9 cm.
Step-by-step explanation:
The length and width of a rectangle as legs form a right triangle with the diagonal of the triangle as the hypotenuse.
We can use the Pythagorean theorem to write an equation.
Let the width = w = leg a
The length = w + 3 = leg b
The diagonal = the hypotenuse = 12 = c
a^2 + b^2 = c^2
w^2 + (w + 3)^2 = 15^2
w^2 + w^2 + 6w + 9 = 225
2w^2 + 6w - 216 = 0
w^2 + 3w - 108 = 0
(w + 12)(w - 9) = 0
w + 12 = 0 or w - 9 = 0
w = -12 or w = 9
Since a width cannot be a negative number, we discard the solution w = -12.
width = w = 9
length = w + 3 = 9 + 3 = 12
Answer: The length is 12 cm, and the width is 9 cm.
