i need help with this problem its not for a test but i dont understand how to solve it

Question

given the length of the sides of a triangle are 2x + 1, 4x - 10, x + 5 and the peimeter is 24 determine the length of all three sides of the triangle the height of the triangle is 8.49 what is the area of the triangle

Answer 1

Your English grammar needs as much help as your math. Sentences begin with a capital letter and end with a period. Questions also begin with a capital letter but end with a question mark. And if you don't think that is important, just write your next job application in the way you have submitted this question and see your result.

I think what you want is:

2x+1 + 4x-10 + x+5 = 24

7x-4=24

x=4

The sides are 9, 6, and 9.

You have not specified the altitude to which side; therefore, it cannot be used to compute the area, You could, of course, compute the area from Heron's formula since you have all 3 sides.

Answer 2

Paul, I'm sometimes as snarky as you. I try not to be, though.

Paul calculates the three sides, two of which are equal.

The altitude to the non-equal side is √(9^2-3^2) = 3√8 = 8.4853, which rounds to 8.49, so the height was the altitude to the non-equal side. You get the altitude from the Pythagorean theorem after bisecting the non-equal side.

The area is 1/2bh; given the altitude of 8.49, we would calculate 1/2 * 6 * 8.49 = 25.47

Using the exact value, we get 1/2 * 6 * 3√8 = 9√8 = 25.4558