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

Answer:

The length of the base is 7 inches.

Step-by-step explanation:

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

$V=\frac{1}{2}lbh$

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

$140=\frac{1}{2}(4)(10)b$

$b=\frac{140*2}{4*10} =7\:inches$

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

The length of the base is 7 inches.

Answer 2

Answer:

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

Step-by-step 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