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the volume of a solid triangular prism is 726 cubic centimeters. its height is 12 centimeters and its bases are congruent right isosceles triangles. find the lengths of the equal sides of each base.

Sagot :

sqdancefan

9514 1404 393

Answer:

  11 cm

Step-by-step explanation:

The volume of the prism is given by the formula ...

  V = Bh

where B is the area of the triangular base, and h is the height.

Filling in the given information, we find the area of the triangular base to be ...

  726 cm³ = B(12 cm)

  B = 726 cm³/(12 cm) = 60.5 cm²

The area of an isosceles right triangle is half the area of a square with the same side lengths:

  B = 1/2s²

  60.5 = 1/2s²

  s = √(2(60.5)) = √121 = 11

The length of each of the equal sides of the base is 11 cm.

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