Does this triangle have a hypotenuse of 39 feet long?

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  no — the hypotenuse is about 33.5 ft long

Step-by-step explanation:

The hypotenuse (h) is given by the Pythagorean theorem.

  h² = 15² +30² = 225 +900 = 1125

  h = √1125 ≈ 33.54

The hypotenuse of this triangle is not 39 feet long.

Additional comment

You can estimate the hypotenuse based on the relative side lengths. Here the short side is 1/2 the length of the long side. This means the hypotenuse will be longer than the long side by an amount between ...

  0.4(1/2)² = 0.1

and

  0.5(1/2)² = 0.125

times the length of the long side. That is, the additional length will be between 3 and 3.75 feet, so the hypotenuse will be shorter than 33.75 feet.

Suppose you want to frame a collage of pictures. You have a 9-ft strip of wood for the frame. What dimensions of the frame give you the maximum area for the collage? What is the maximum area?

A:

Perimeter = 2(L + W) 9 = 2(L+W) L+W = 4.5 L = 4.5-W Area = LW Area = (4.5-W)W A = 4.5W - W^2 You have a quadratic with a = -1 and b = 4.5 Maximum area occurs when W = -b/(2a) = 4.5/(2*-1) = 2.25  

Step-by-step explanation: