Question

is this a right triangle? lets use the pythagorean theorem to check. start by substituting the two shorter side lengths for a and b, and the longest side length for c in the equation.

(image of a triangle with sides 7 cm, 6 cm, 5 cm)

$a^2 + b^2 = c^2$
$\square^2 + \square^2 \stackrel{?}{=} \square^2$

Explanation:

Step1: Identify a, b, c

The two shorter sides (legs) are 5 cm and 6 cm, so \( a = 5 \), \( b = 6 \). The longest side (hypotenuse) is 7 cm, so \( c = 7 \).

Step2: Substitute into Pythagorean Theorem

Substitute into \( a^2 + b^2 = c^2 \): \( 5^2 + 6^2 \stackrel{?}{=} 7^2 \).

Step3: Calculate each term

\( 5^2 = 25 \), \( 6^2 = 36 \), \( 7^2 = 49 \).

Step4: Check equality

Left side: \( 25 + 36 = 61 \). Right side: \( 49 \). Since \( 61
eq 49 \), the triangle is not right - angled. But for the substitution step, the boxes should be filled with 5, 6, 7.

Answer:

The boxes should be filled as \( \boldsymbol{5}^2+\boldsymbol{6}^2\stackrel{?}{=}\boldsymbol{7}^2 \)