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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!

Guest Mar 19, 2018

Best Answer 

 #1
avatar+7339 
+2

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

hectictar  Mar 19, 2018
 #1
avatar+7339 
+2
Best Answer

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

hectictar  Mar 19, 2018

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