in order for three line segments to form a triangle with non-zero area, they must satisfy the "triangle inequality." there are several ways to express this, but perhaps the simplest is
a + b > c
where a, b, and c are the lengths of sides in order from shortest to longest.
here, that means the requirement for a triangle is
4 + 4 > 7 . . true, so a triangle can be formed
the triangle inequality is satisfied by these segment lengths.
d. 150 feet
the formula for the area of a rectangle is: area = lw, where l = length and w = width. in this case, the length is defined as '90 feet more than twice the width' or l = 2w + 90. if we put this expression in for the value of 'l' in our formula for area we get:
area = w(2w +90), distribute: area = 2w² + 90w = 58500
subtracting 58500 from both sides, we get the following polynomial:
2w² + 90w - 58500
we can divide all the terms by '2' to simplify:
w² + 45w - 29250
next, we look for the two factors of 29,250 that will add up to 45, which is -150 and +190 to factor our polynomial:
(w - 150)(w + 190) = 0
setting both equations equal to 0 and solving for w:
w - 150 = 0 or w = 150
w + 190 = 0 or w = -190
since our with can not be negative, then the correct width of the field is 150 ft.