Example 6

A large terrarium is used to display a box turtle in a pet store. The terrarium has the shape of a rectangular prism with a volume of 8748 cubic inches. The dimensions of the terrarium are shown. Find the length, width, and height of the terrarium.

TERRARIUM

Solve a multi-step problem

Example 6 Solve a multi-step problem

STEP 2 Solve the equation for w.

( )36+w8748 ( )w ( )9w –= Write equation.

w3 27w20 = + – 324w – 8748 Multiply. Subtract 8748 from each side.

SOLUTION

STEP 1 Write a verbal model. Then write an equation.

8748 ww 36+( )= • • w 9( )–

Example 6 Solve a multi-step problem

( )27w2+w3= ( )8748+324w–0 Group terms.

( )27+ww2 ( )27+w324–0 = Factor each group.

0 = ( )324w2 – ( )27w + Distributive property

0 = ( )18w + ( )27w +( )18w – Difference of two squares pattern

018w =–018w =+ 027w =+or or Zero-product property

–18w = –27w =18w =or or Solve for w.

Because the width cannot be negative, the only solution is 18w =

Example 6 Solve a multi-step problem

STEP 3 Find the length and height.

=36w + 3618 + 54=Length

Height 9w –= = 918 – = 9

ANSWER

The length is 54 inches, the width is 18 inches, and the height is 9 inches.

Guided Practice

ANSWER 3 ft long by 2 ft wide by 12 ft high

for Example 6

13. DIMENSIONS OF A BOXA box in the shape of a rectangular prism has a volume of 72 cubic feet. The box has a length of x feet, a width of feet, and a height of feet. Find the dimensions of the box.

( )1x – ( )9x +