Triangle area

[gcooper]

The height of a triangle is 12m longer than the base. Its area is 54m^2, find the lengths of the base and height.

So, I tried approaching it this way:

1/2 * x * (x + 12) = 54

1/2 * x^2 + 12x = 54

x^2 + 24x = 108

x^2 + 24x - 108 = 0

So, now I'm stuck, because I can't find 2 numbers to add to 24 and to multiply to -108. Where and what did I do wrong?

 

[stapel]

Thank you for showing your work and reasoning so nicely!

The height of a triangle is 12m longer than the base. Its area is 54m^2, find the lengths of the base and height.

So, I tried approaching it this way:

1/2 * x * (x + 12) = 54

You're good to here.

1/2 * x^2 + 12x = 54

It looks like you distributed the x through the parentheses, but not the 1/2. It should be:

. . . . .(1/2)(x)(x + 12) = (1/2)(x)(x) + (1/2)(x)(12)

Simplify, and continue....

 

[wjm11]

The height of a triangle is 12m longer than the base. Its area is 54m^2, find the lengths of the base and height.

So, I tried approaching it this way:

1/2 * x * (x + 12) = 54

1/2 * x^2 + 12x = 54

x^2 + 24x = 108

x^2 + 24x - 108 = 0

So, now I'm stuck, because I can't find 2 numbers to add to 24 and to multiply to -108. Where and what did I do wrong?

Your work and approach look fine. This quadratic does not factor nicely. If you are expecting to get "nice" answers, check the problem statement and make sure you are using the right numbers.

Even though this won't factor nicely, you can still solve it using the quadratic formula. You should get one negative and one positive value for x. Only the positive answer applies for this problem.

 

[HallsofIvy]

Did you not read Stapel's response? He posted nearly 24 hours before you did, pointed out exactly what the original poster did wrong and gcooper's "work and approach" were NOT "fine". Solving the equation as you suggest will NOT give the correct answer.

 

[wjm11]

Did you not read Stapel's response? He posted nearly 24 hours before you did, pointed out exactly what the original poster did wrong and gcooper's "work and approach" were NOT "fine". Solving the equation as you suggest will NOT give the correct answer.

Of course I read Stapel's response, Halls.

The OP did handle the 1/2 by multiplying both sides of the equation. Unfortunately, when he correctly doubled the 54 to 108, he also (incorrectly) doubled the 12 into 24. This was not specifically addressed in the first response.

While Stapel's answer is obviously a correct approach, it did not address the appearance of 108 in the OP's work. I also was trying to decipher the steps the OP was taking but did not catch the change to 24. Thank you for causing me to re-examine the problem.

Gcooper, if you correct your 24 back to 12, (x^2 + 12x - 108 = 0), you'll get some "nice" answers for x (-18 and 6). Your triangle base is 6.