We know the heights of two similar rectangular prisms but the length and width of just one of them.
Recall that similar solids are solids that have the same shape and proportional corresponding dimensions. Therefore, the ratio between corresponding dimensions is constant. We can use this information to write a proportion. We want to find the value of l, and w. Let's do this one at time.
Value of l
We know that a rectangular prism with a length of 4.6 centimeters and a height of 6.4 centimeters is similar to a rectangular prism with a length of l and a height of 16 millimeters.
Height of bigger prism/Height of smaller prism
=
Length of bigger prism/Length of smaller prism
Note that the height of the bigger prism is 6.4 centimeters, so we need to covert this unit to millimeters. We know that there are 10 millimeters in 1 centimeter. Therefore, the height is 6.4 * 10=64 millimeters and the length is 46 millimeters. Let's substitute the corresponding dimensions into the equation and solve for l.
Height of bigger prism/Height of smaller prism=Length of bigger prism/Length of smaller prism
The length of the small rectangular prism l is 11.5 millimeters.
Finding w
We know that a rectangular prism with a width of 4.6 centimeters and a height of 6.4 centimeters is similar to a rectangular prism with a width of w and a height of 16 millimeters.
Height of bigger rectangular prism/Height of small rectangular prism
=
Width of bigger rectangular prism/Width of small rectangular prism
Note that the height of the bigger prism is 6.4 centimeters, we need to covert this unit to millimeters. We know that there are 10 millimeters in 1 centimeter. Therefore, the height is 6.4 * 10=64 millimeters and the width is 46 millimeters. Let's substitute the corresponding dimensions into this equation and solve for l.
Height of bigger prism/Height of smaller prism=Width of bigger prism/Width of smaller prism
