Answer:
width = 8 in
height = 15 in
Step-by-step explanation:
considering the pythagorous theorem
[tex]hypotenuse^{2} = height^{2} +base^{2}\\[/tex]
hypotenuse = length of diagonal = 17 in
base = width = w
height = L = 2w -1
[tex](17)^{2}=(2w-1)^{2}+w^{2}\\289 = 4w^{2}-4w+1+w^{2}\\288=5w^{2}-4w\\5w^{2}-4w-288=0[/tex]
applying the quadratic formula two roots for w:
[tex]w=\frac{-b \pm \sqrt{b^{2}-4ac} }{2a}\\b = -4\\a= 5\\c= -288\\w=\frac{-(-4) \pm \sqrt{(-4)^{2}-4(5)(-288)} }{2(5)}[/tex]
w = 8 ; w = -7.2
as width cannot be negative
so
w = 8 in
L = 2w -1
L = 16 -1
L = 15 in
