How do I solve this word problem?

Question

A triangular base prism has a volume of 16.2 cubic centimeters. The base is an isosceles right triangle. The height of the prism is 10 centimeters. What is the approximate length of the hypotenuse of the triangular base of the prism? And I need an explanation of how.

Answer 1

Hi Mika.

 

The volume of an object is the area of its base times its height.

 

V = A*h

 

Your job in this question is to figure out the area of the base, since they already gave you the volume and the height.

 

16.2 = A*10

A = 1.62

 

The base is an isosceles triangle. We can call both side lengths of our triangle x, since it's an isosceles triangle. Therefore its side lengths are equal. The area of the triangle is 1/2*b*h.

 

A = 1/2*x^2

 

So

 

1/2*x^2 = 1.62

 

x^2 = 3.24

 

x = 1.8

 

An isosceles right triangle has 45 degree angles. The hypotenuse of a 45-45-90 triangle will have a length that is √(2) times larger than the side lengths.

 

So, the hypotenuse length will be

 

1.8√(2) = ~2.55

 

Hope this helps.