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

Answer:

Therefore,

The lengths of side a and b are,

$a=2\ mm\\b=4\ mm$

Step-by-step 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,

$\textrm{Volume of the Triangular Prism}=\dfrac{1}{2}\times Length\times Width\times Height$

Substituting the given values we get

$40=\dfrac{1}{2}\times a\times 2a\times 10\\\\2a^{2}=8\\\\a^{2}=4\\square\ rooting\\\\a=\sqrt{4}=2\ mm$

But ,

$b = 2a$     Given

Substituting a we get

$b = 2\times 2=4\ mm$

Therefore,

The lengths of side a and b are,

$a=2\ mm\\b=4\ mm$