Chapter 8.3, Problem 26PPS

To determine

To determine if the highlighter fit in the given box.

Answer to Problem 26PPS

The triangle can easily fit the rectangular box.

Explanation of Solution

Given information :

Equilateral triangle with side 9 cm is given.

Here we shall find the height of the equilateral triangle.

When we draw an altitude in equilateral triangle we know that it divides the triangle into two same triangles.

Hence the height of the triangle is given by,

$\begin{array}{l}\sin {60}^{\circ }=\frac{\text{Opposite}}{\text{Hypotenuse}}\\ \frac{\sqrt{3}}{2}=\frac{h}{9}\\ h=\frac{9\sqrt{3}}{2}=7.8cm\end{array}$

Now the height of the box is 7 in. or 48.2 cm.

Hence we can determine that the triangle can easily fit the rectangular box.