To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

3a⁹ + 7a⁹ = 10a⁹

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 = \( \sqrt{a} \) = \( \sqrt{4} \) = 2

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 = 2² + 2²
c² = 8
c = \( \sqrt{8} \) = \( \sqrt{4 x 2} \) = \( \sqrt{4} \) \( \sqrt{2} \)
c = 2\( \sqrt{2} \)

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

p = x + y + z
p = 10cm + 13cm + 5cm = 28cm

Perimeter is equal to the sum of the four sides:

p = a + b + c + d
p = 3 + 1 + 3 + 5
p = 12

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

c² = a² + b²
c² = 2² + 6²
c² = 4 + 36
c² = 40
c = \( \sqrt{40} \)