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

p = x + y + z
p = 10cm + 15cm + 6cm = 31cm

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

7b - 4x = -7b - 2x - 7
7b = -7b - 2x - 7 + 4x
7b + 7b = -2x - 7 + 4x
14b = 2x - 7
b = \( \frac{2x - 7}{14} \)
b = \( \frac{2x}{14} \) + \( \frac{-7}{14} \)
b = \(\frac{1}{7}\)x - \(\frac{1}{2}\)

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 first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

a² + 10a - 6 = 4a + 1
a² + 10a - 6 - 1 = 4a
a² + 10a - 4a - 7 = 0
a² + 6a - 7 = 0

Next, factor the quadratic equation:

a² + 6a - 7 = 0
(a - 1)(a + 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 1) or (a + 7) must equal zero:

If (a - 1) = 0, a must equal 1
If (a + 7) = 0, a must equal -7

So the solution is that a = 1 or -7