According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 4² + 6²
c² = 16 + 36
c² = 52
c = \( \sqrt{52} \)

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

You need to find the value of a so solve the first equation in terms of y:

-4a + y = 3
y = 3 + 4a

then substitute the result (3 - -4a) into the second equation:

-3a - 9(3 + 4a) = -6
-3a + (-9 x 3) + (-9 x 4a) = -6
-3a - 27 - 36a = -6
-3a - 36a = -6 + 27
-39a = 21
a = \( \frac{21}{-39} \)
a = -\(\frac{7}{13}\)

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with a° = 18, the value of c° is 18.

Perimeter is equal to the sum of the four sides:

p = a + b + c + d
p = 1 + 1 + 7 + 2
p = 11