An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.

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\( \sqrt{2} \)

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -20 as well and sum (Inside, Outside) to equal 1. For this problem, those two numbers are -4 and 5. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + y - 20
y² + (-4 + 5)y + (-4 x 5)
(y - 4)(y + 5)

A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.

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

c² = a² + b²
c² = 5² + 7²
c² = 25 + 49
c² = 74
c = \( \sqrt{74} \)