Question

A triangular boat's sail has a total area of 7 square inches.

If the height of the sail is 3 inches less than twice the
length of its base, then find the length of the base and
height.

Answer 1

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

Answer 2

Answer: b = 3.5, h = 4

Step-by-step explanation: a = 1/2bh, area of a triangle formula

7 = 1/2((b)(2b-3)) state h in terms of b

7 = 1/2(2b^2-3b) simplify

7 = b^2 - 1.5b simplify

b = 3.5 final answer

Then, solve for h.

h = 7 - 3 substitute

h = 4 final answer

hope this helps!