Answer:
9 in × 5 in
Step-by-step explanation:
the area of a rectangle :
length × width
and this is 45 in² in our case.
the perimeter of a rectangle is
2×length + 2×width
and this is 28 in in our case.
l×w = 45
l = 45/w
2×l + 2×w = 2×(45/w) + 2w = 28
45/w + w = 14
45 + w² = 14w
w² - 14w + 45 = 0
the general solution to such a squared equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = w
a = 1
b = -14
c = 45
w = (14 ± sqrt((-14)² - 4×1×45))/(2×1) r
= (14 ± sqrt(196 - 180))/2 = (14 ± sqrt(16))/2 =
= (14 ± 4)/2 = 7 ± 2
w1 = 7 + 2 = 9 in
w2 = 7 - 2 = 5 in
l1 = 45/w1 = 45/9 = 5 in
l2 = 45/w2 = 45/5 = 9 in.
so, we see, length and width are interchangeable. it is only important to make one 9 in and the other 5 in.
