Explanation:
area of a triangle
base × height / 2
in our case
base × height / 2 = 7
base × height = 14
height = 2×base - 3
we can use the last identity in the area equation and get
base × (2×base - 3) = 14
2×base² - 3×base - 14 = 0
the solution to a quadratic equation like
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
base = (3 ± sqrt((-3)² - 4×2×-14))/(2×2) =
= (3 ± sqrt(9 + 112))/4 = (3 ± sqrt(121))/4 =
= (3 ± 11)/4
base1 = (3 + 11)/4 = 14/4 = 7/2 = 3.5 in
base2 = (3 - 11)/4 = -8/4 = -2
negative numbers for sizes of physical objects don't make sense, so, base = 3.5 in is our solution.
height = 2×base - 3 = 2×3.5 - 3 = 7 - 3 = 4 in
base length = 3.5 in
height = 4 in