Question

A gift box in the shape of a triangular prism has a volume of

140 cubic inches, a base height of 10 inches, and a height
of 4 inches. What is the length of the base?

Answer 1

Hence the length of the base is given by 7 inches.

Explanation:

Given:

Volume of a triangular prism=140 ci

Height=4 inches

base height =10 inches.

To Find:

Length of base

Solution:

We know that ,

Volume of triangular prism is given by

V=1/2(base *height* length)=1/2*b*h*l

Here V=140 ci

b=10 inches ,h=4 inches.

140=1/2*(10*4*l)

280=40l

l=280/40

l=7 inches

Answer 2

The length of the base is 7 inches.

Explanation:

A triangular prism with base height
`h`, length
`l`, and base length
`b` has volume
`V` given by

`V=(1)/(2)lbh`

We are told that the volume of the prism is 140 cubic inches, and
`h=10`,
`l=4`; therefore we have:

`140=(1)/(2)(4)(10)b`

`b=(140*2)/(4*10) =7\:inches`

`\boxed{b=7\:inches}`

The length of the base is 7 inches.