Question

A book shelf has supports as shown in the diagram. What is the length of the wall support?

Answer 1

Observe that the triangle has a square angle.

So the triangle is a right angled triangle, and hence the Pythagoras Theorem is applicable.

$\text{Base}^2+Height^2=Hypotenuse^2$

Substitute the values,

$12^2+Height^2=15^2\Rightarrow Height^2=225+144\Rightarrow Height=9$

Thus, the height i.e. length of the wall support is 9 inches.