To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses.

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{25} \) = 5

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 5² + 5²
c² = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 5cm + 15cm + 7cm = 27cm

The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 31° - 66° = 83°

To solve this equation, isolate the variable for which you are solving (c) on one side of the equation and put everything else on the other side.

9c - 8y = c - y - 9
9c = c - y - 9 + 8y
9c - c = -y - 9 + 8y
8c = 7y - 9
c = \( \frac{7y - 9}{8} \)
c = \( \frac{7y}{8} \) + \( \frac{-9}{8} \)
c = \(\frac{7}{8}\)y - 1\(\frac{1}{8}\)