Let's begin with recalling the 30^(∘)-60^(∘)-90^(∘) Triangle Theorem. This theorem tells us that the length of the hypotenuse of this right triangle is 2 times the length of the shorter leg s, and the length of the longer leg is sqrt(3) times the length of the shorter leg.
Now let's take a look at the given picture. We will draw an altitude of an equilateral triangle highlighter. Let h represent this altitude.
Notice that after drawing an altitude we have the 30^(∘)-60^(∘)-90^(∘) Triangle. Therefore, the shorter leg of this triangle has a length two times less than 9.
Next, according to the recalled theorem, we know that the longer leg, h, is sqrt(3) times the length of the shorter leg.
h=4.5*sqrt(3)≈ 7.79
This means that the height of the highlighter is approximately 7.79 centimeters. To determine whether this highlighter will fit the rectangular box let's compare the height of this box, which is 7 centimeters, with the height of the highlighter.
7<7.79
Since the height of the highlighter is greater than the height of the box, it will not fit this rectangular box.
