Question

The figure shows a Square and 4 congruent isosceles triangles the lenght of leg x is 12 feet,What is the lenght in feet of the hypnotese of each triangle?

Answer 1

Pythagoras theorem

In order to find the hypotenuse of each triangle we are going to focus on the sides of one of them:

Since the figure in the center is a square then all its sides lenght is 10 feet:

Since the triangle is divided in halfs, then:

Now we can find its hypotenuse. We have the following triangle:

We know, by the Pythagoras Theorem, that:

$\begin{gathered} x^2+y^2=hypotenuse^2 \\ \downarrow \\ 12^2+5^2=hypotenuse^2 \\ \downarrow \\ 144^{}+25^{}=hypotenuse^2 \\ 169=hypotenuse^2 \end{gathered}$

Since,

13² = 169

then

13² = hypotenuse²

Then

13 = hypotenuse

Answer- the hypotenuse of each triangle is 13ft