Chapter 8.3, Problem 4CYP

To determine

To calculate: How to find the distance from vertex B to side AC and also to find the length of other sides of isosceles right triangle

Answer to Problem 4CYP

The distance from vertex $B$ to longest side $AC$ is approximately $53$ centimetres and measure of other two sides is approximately $76$ centimetres

Explanation of Solution

Given: Below is an aquarium coffee table such that top of table has shape of isosceles right triangle. Also, length of table’s longest side AC measures $107$ centimetres

  

Formula Used:

In an isosceles right triangle, longest side is hypotenuse, and other sides are equal

Calculation:

Given that a top of the aquarium coffee is an isosceles right triangle

Thus, in triangle ABC

Sides AB and BC are equal, and $\angle ABC$ is a right angle

Therefore, in $△ABC$ :

  $A{B}^2+B{C}^2=A{C}^2$

Substituting the values:

  $\begin{array}{l}A{B}^2+A{B}^2=A{C}^2\\ 2A{B}^2={107}^2\\ 2A{B}^2=11449\\ A{B}^2=5724.5\\ AB=75.660\\ AB\approx 76\end{array}$

Thus, other two sides of table measure approximately $76$ centimetre.

In an isosceles triangle, side from vertex perpendicular to line divides the side

Thus, in right triangle ABD

  $\begin{array}{l}B{D}^2+A{D}^2=A{B}^2\\ B{D}^2+{53.5}^2={75.6}^2\\ B{D}^2=5715.36-2862.25\\ BD=53.41\end{array}$

Conclusion:

Hence, distance from vertex $B$ to longest side $AC$ is approximately $53$ centimetres and measure of other two sides is approximately $76$ centimetres