Question

The triangular base of a prism is a right triangle with sides a and b. B= 2a. The height of the prism is 10mm and it's volume is 40mm^3 Find the lengths of side a and b

Answer 1

Therefore,

The lengths of side a and b are,

`a=2\ mm\\b=4\ mm`

Explanation:

Given:

Shape is of triangular prism.

Length = a

Width = b

Height = h =10 mm

Also, b = 2a

Volume of the Triangular Prism = 40 mm³

To Find:

a = ?

b =?

Solution:

Shape is of triangular prism. GIVEN

We Know that,

`\textrm{Volume of the Triangular Prism}=(1)/(2)* Length* Width* Height`

Substituting the given values we get

`40=(1)/(2)* a* 2a* 10\\\\2a^(2)=8\\\\a^(2)=4\\square\ rooting\\\\a=√(4)=2\ mm`

But ,

`b = 2a` Given

Substituting a we get

`b = 2* 2=4\ mm`

Therefore,

The lengths of side a and b are,

`a=2\ mm\\b=4\ mm`