Answer:
the width is 10 m
Step-by-step explanation:
if the relationship between area and width is
A = 80*w − w²
for an area A=700 m² , we have
700 m² = 80*w − w²
w² - 80*w + 700 m² = 0
aw² + b*w + c = 0
where a=1 , b=-80 and c=700
this quadratic equation has as solution the following formula
w = [-b ± √ ( b² - 4*a*c) ]/(2*a)
replacing values
w = [80 ± √ ( 80² - 4*1*700) ]/(2*1) = (80 ± 60)/2
then
w₁=(80 - 60)/2 = 10 m
w₂ =(80 + 60)/2 = 70 m
since the area has the form A= length * width = 80*w − w² = (80− w)*w
then the length of the rectangle is
length = 80− w
for w₁=10 m → length = 80− 10 = 70 m
for w₁=70 m → length = 80− 70 = 10 m
by definition the shorter side is the width ( and the longer one , the length) , therefore the only possible option is the first one .
Thus the width is 10 m
