Question

A SQUARE RECTANGULAR PRISM (BASE IS A SQUARE) HAS A
VOLUME OF 38 CU. IN. THE HEIGHT IS 10 LESS THAN THE AREA
OF THE BASE. WHAT IS THE HEIGHT? NO UNITS.

Answer 1

The height of the prism $\approx 2.9$

The whole volume of the prism is

$\text{Volume} = \text{Area of base}\times \text{Height}$

Here, the volume is 38 cu. in.

From the question, the area and the height are related as follows;

$\text{Height} = \text{Area} - 10 \implies \text{Height + 10} =\text{Area}$

Substituting this into the formula for the volume, we get

$\text{Volume}=(\text{Height} +10)\times \text{Height}=38\\\\\text{Height}^2 + 10\times\text{Height}=38\\\\\text{Height}^2 + 10\times\text{Height}-38=0$

If the above quadratic equation is solved for the height, we get

$\text{Height}\approx 2.9$

(We can't take the other solution since height has to be greater than zero)

Another word problem on volume can be found in this link: https://brainly.com/question/17142547