An architect wants to do a rectangle with the diagonal of 25 inches the length of the rectangle is to be 3 inches more than triple the width. What is the dimensions she should make the rectangle

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

step-by-step explanation:

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