Question

a rectangle is drawn so the width is 17 inches longer than the height. if the rectangle's diagonal measurement is 53 inches, find the height.

Answer 1

The height is 45 width.

What is rectange?

• A quadrilateral with four right angles is a rectangle.
• It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°).
• A square is a rectangle with four equal sides.

solving-

• Let the height be "x".
• Then width = "x+17".
• Pythagoras:
• x^2 + (x+17)^2 = 53^2
• x^2 + x^2 + 34x + 289 = 2809
• 2x^2 + 34x - 2520 = 0
• x^2 + 17x - 1260 = 0
• x = [-17 +- sqrt(17^2-4*-1260)]/2
• x = [-17 +- sqrt(5329)]/2
• Positive solution:
• x = [-17+73]/2
• x = 28 (height)
• x+17 = 45 (width)

Hence, The height is 45 width.

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