Answer: The length is 24 inches. The width is 7 inches.
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
The length of the rectangle is to be 3 inches more than triple the width. This means that
L = 3W + 3
The diagonal of the rectangle divides it into two right angle triangles and the diagonal represents the hypotenuse. The length and width represents the opposite and adjacent side. Applying Pythagoras theorem,
Hypotenuse² = opposite side² + adjacent side²
Therefore,
25² = L² + W²
625 = L² + W² - - - - - - - - - -1
Substituting L = 3W into equation 1, it becomes
625 = (3W + 3)² + W²
625 = 9W² + 9W + 9W + 9 + W²
10W² + 18W - 625 + 9 = 0
10W² + 18W - 616 = 0
Dividing through by 2, it becomes
5W² + 9W - 308= 0
5W² + 44W - 35W - 308 = 0
W(5W + 44) - 7(5W + 44) = 0
W - 7 = 0 or 5W + 44 = 0
W = 7 or W = - 44/5
Since the width cannot be negative, then W = 7
L = 3W + 3 = 7 × 3 + 3
L = 24
