A toy is made up of nesting boxes. The smallest box has dimensions of 102.2 cm by 108.4 cm by 206.1 cm. If the largest box is created by dilating the smallest box by a scale factor of 3.5, what are the largest box's dimensions? Break down the explain

Answer 1

First, we need to multiply each dimension of the smallest box by the scale factor (3.5) to find the dimensions of the largest box.

For the length:
102.2 cm * 3.5 = 357.7 cm

For the width:
108.4 cm * 3.5 = 379.4 cm

For the height:
206.1 cm * 3.5 = 721.35 cm

Therefore, the largest box has dimensions of 357.7 cm by 379.4 cm by 721.35 cm.

Explanation:
When dilating an object, each dimension of the object is multiplied by the scale factor to find the new dimensions of the dilated object. In this case, multiplying each dimension of the smallest box by 3.5 gave us the dimensions of the largest box. This means that the largest box is 3.5 times larger in each dimension compared to the smallest box.