This is the the triangle ABC
AS=x cm
BS= x cm
CS = (x-2) cm
You can calculate the (Surface? Area? Not sure what the correct term in English is...) with the formula x^2-2x
a. Solve the equatation x^2-2x=24
b. What does the solution of a. mean? What does this mean for the height of the triangle?
c. The surface of the triangle is 120 square cm. Calculate the length of AB
I'm horrible at these kind of math questions, I'd really appreciate the help!
+9466 a. Solve the equation x2 - 2x = 24
x2 - 2x = 24
Subtract 24 from both sides of the equation.
x2 - 2x - 24 = 0
Factor the left side. What two numbers add to -2 and multiply to -24 ? -6 and +4
(x - 6)(x + 4) = 0
Set each factor equal to zero.
x - 6 = 0 or x + 4 = 0
x = 6 or x = -4
b. It means...
The two possible values of x that make the area of the triangle be 24 square cm are 6 and -4 .
However, since x is a length, we can exclude the negative possibility.
So x must be 6 .
When x is 6 , the area of the triangle is 24 square cm.
the height of the triangle = (x - 2) cm = (6 - 2) cm = 4 cm
c.
area of the triangle = x2 - 2x
Plug in 120 for the area of the triangle.
120 = x2 - 2x
Subtract 120 from both sides of the equation.
0 = x2 - 2x - 120
Factor the right side of the equation.
0 = (x - 12)(x + 10)
Set each factor equal to zero.
x - 12 = 0 or x + 10 = 0
x = 12 or x = -10
Exclude the negative possibility.
x = 12
length of AB = 2 * x = 2 * 12 = 24 cm
+9466 a. Solve the equation x2 - 2x = 24
x2 - 2x = 24
Subtract 24 from both sides of the equation.
x2 - 2x - 24 = 0
Factor the left side. What two numbers add to -2 and multiply to -24 ? -6 and +4
(x - 6)(x + 4) = 0
Set each factor equal to zero.
x - 6 = 0 or x + 4 = 0
x = 6 or x = -4
b. It means...
The two possible values of x that make the area of the triangle be 24 square cm are 6 and -4 .
However, since x is a length, we can exclude the negative possibility.
So x must be 6 .
When x is 6 , the area of the triangle is 24 square cm.
the height of the triangle = (x - 2) cm = (6 - 2) cm = 4 cm
c.
area of the triangle = x2 - 2x
Plug in 120 for the area of the triangle.
120 = x2 - 2x
Subtract 120 from both sides of the equation.
0 = x2 - 2x - 120
Factor the right side of the equation.
0 = (x - 12)(x + 10)
Set each factor equal to zero.
x - 12 = 0 or x + 10 = 0
x = 12 or x = -10
Exclude the negative possibility.
x = 12
length of AB = 2 * x = 2 * 12 = 24 cm
