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 = \( \sqrt{a} \) = \( \sqrt{49} \) = 7

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 = 7² + 7²
c² = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

y² + 18y + 81 = 0
(y + 9)(y + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, (y + 9) must equal zero:

If (y + 9) = 0, y must equal -9

So the solution is that y = -9

A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.

The area of a parallelogram is equal to its length x width:

a = l x w
a = a x b
a = 5 x 7
a = 35

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 -45 as well and sum (Inside, Outside) to equal 4. For this problem, those two numbers are -5 and 9. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 4y - 45
y² + (-5 + 9)y + (-5 x 9)
(y - 5)(y + 9)