Step-by-step explanation:
#27 Using Pythagorean theorem, the length of side ZY is given by
(ZY)^2 = (x - 1)^2 + (x + 1)^2 = (x^2 -2x + 1) + (x^2 + 2x + 1)
= 2x^2 + 2
Taking the square root,
[tex]zy = \sqrt{2 {x}^{2} + 2} [/tex]
#28 There are two shapes that make up this figure: a square of side x and a rectangle with sides (x + 6) and (2x - 3 - x) or (x - 3). Therefore, the area of this figure is
A = area of square + area of rectangle
= (x^2) + (x + 6)(x - 3)
= x^2 + (x^2 + 3x - 18)
= 2x^2 + 3x - 18
