A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.

An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

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

8a + 4y = 3a + 3y + 3
8a = 3a + 3y + 3 - 4y
8a - 3a = 3y + 3 - 4y
5a = -y + 3
a = \( \frac{-y + 3}{5} \)
a = \( \frac{-y}{5} \) + \( \frac{3}{5} \)
a = -\(\frac{1}{5}\)y + \(\frac{3}{5}\)

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\( \sqrt{2} \)