The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 1 x 3 = \( \frac{3}{2} \) = 1\(\frac{1}{2}\)

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 = \( \sqrt{a} \) = \( \sqrt{81} \) = 9

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 = 9² + 9²
c² = 162
c = \( \sqrt{162} \) = \( \sqrt{81 x 2} \) = \( \sqrt{81} \) \( \sqrt{2} \)
c = 9\( \sqrt{2} \)

An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.

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:

c² - 5c + 17 = 5c - 4
c² - 5c + 17 + 4 = 5c
c² - 5c - 5c + 21 = 0
c² - 10c + 21 = 0

Next, factor the quadratic equation:

c² - 10c + 21 = 0
(c - 3)(c - 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 3) or (c - 7) must equal zero:

If (c - 3) = 0, c must equal 3
If (c - 7) = 0, c must equal 7

So the solution is that c = 3 or 7

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

p = x + y + z
p = 6cm + 13cm + 15cm = 34cm