A triangular sail has an area of x^2 + 5x + 6 square meters and a height of x + 3 meters. Find the length of the sail's base.
2007-08-01 18:19:11 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The formula for the area of a triangle is:
Area = 1/2 * Base * Height
Height = x+3
x^2 + 5x + 6 = Base/2 * (x+3)
x^2 + 5x + 6 is a polynomial equation. To solve this, try to find two values whose sum is +5 and product is +6. They are +2 and +3. So:
x^2 + 5x + 6 = (x+2) * (x+3)
Therefore:
(x+2) * (x+3) = Base/2 * (x+3)
We will transfer (x+3) from the right side as the factor to the left side as the denominator:
((x+2) * (x+3)) / (x+3) = Base/2
x+2 = Base / 2
(x + 2) * 2 = Base
Base = 2x + 4
So Base is 2x+4 for whatever value the "x" is equal to.
Good luck.
2007-08-01 18:33:07 · answer #1 · answered by ¼ + ½ = ¾ 3 · 0⤊ 0⤋
Area = 1/2 bh = x^2+5x+6 =(x+3)(x+2) if the first term is the height then 1/2 of base = x+2 so base is 2(x+2) = 2x+4
2007-08-01 18:27:54 · answer #2 · answered by 037 G 6 · 0⤊ 0⤋
Area = 1/2 * base * height = x^2 + 5x + 6
= (x+2)(x+3)
Height is x+3, so base = 2*(x+2) = 2x+4
.
2007-08-01 18:25:03 · answer #3 · answered by tsr21 6 · 0⤊ 0⤋
the base len. is 2(x+2) since the area can be facto. as (x+2)(x+3)
and we know that 1/2*b*h=area.
so the ans is 2(x+2)
2007-08-01 19:21:01 · answer #4 · answered by shas 2 · 0⤊ 0⤋