Question

1. 3 ft, 4 ft, 6 ft triangle. $a^2 + b^2 = c^2$. $\square^2 + \square^2 \underline{\underline{?}} \square^2$, $\square + \square \underline{\underline{?}} \square$, $\square \circ \square$. is the triangle a right triangle? $\square$

Explanation:

Step1: Identify sides for Pythagorean theorem

In a right triangle, \(a\) and \(b\) are the legs, \(c\) is the hypotenuse (longest side). Here, legs are 3 ft and 4 ft, hypotenuse is 6 ft? Wait, no, wait: Wait, 3, 4, 6? Wait, no, let's check. Wait, the legs should be 3 and 4, hypotenuse should be 5 (since \(3^2 + 4^2 = 9 + 16 = 25 = 5^2\)), but here the hypotenuse is given as 6? Wait, maybe I misread. Wait, the triangle has sides 3 ft, 4 ft, 6 ft? Wait, no, the diagram: vertical side 3 ft, horizontal side 4 ft, hypotenuse 6 ft? Wait, but let's proceed. So \(a = 3\), \(b = 4\), \(c = 6\)? Wait, no, hypotenuse should be the longest side, so 6 is longer than 4 and 3, so \(c = 6\), \(a = 3\), \(b = 4\).

So substitute into \(a^2 + b^2 = c^2\): \(3^2 + 4^2 \stackrel{?}{=} 6^2\)

Step2: Calculate each square

\(3^2 = 9\), \(4^2 = 16\), \(6^2 = 36\)

Step3: Add the squares of legs

\(9 + 16 = 25\)

Step4: Compare to square of hypotenuse

Now, compare 25 and 36. So \(25
eq 36\)

Answer:

First row: \(3^2 + 4^2 \stackrel{?}{=} 6^2\)
Second row: \(9 + 16 \stackrel{?}{=} 36\)
Third row: \(25
eq 36\)
Is the triangle a right triangle? No (because \(3^2 + 4^2
eq 6^2\))