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

c² = a² + b²
c² = 7² + 6²
c² = 49 + 36
c² = 85
c = \( \sqrt{85} \)

You need to find the value of c so solve the first equation in terms of z:

-7c + z = 9
z = 9 + 7c

then substitute the result (9 - -7c) into the second equation:

8c - 8(9 + 7c) = 2
8c + (-8 x 9) + (-8 x 7c) = 2
8c - 72 - 56c = 2
8c - 56c = 2 + 72
-48c = 74
c = \( \frac{74}{-48} \)
c = -1\(\frac{13}{24}\)

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

a = l x w
a = a x b
a = 6 x 1
a = 6

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.

7a + 8a = 15a

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 = \( \sqrt{a} \) = \( \sqrt{64} \) = 8

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 = 8² + 8²
c² = 128
c = \( \sqrt{128} \) = \( \sqrt{64 x 2} \) = \( \sqrt{64} \) \( \sqrt{2} \)
c = 8\( \sqrt{2} \)