Can you solve this problem:
Identify the letter of the choice that best completes the statment or answer the question.
Note: Since there is no symbol on the keyboard for the right angle sign I will use the greater than sign(<)right angle. The greather/less than sign for the (<>)for a triangle symbol.
m<A=9x-7,m<B=7x-9,and m<C=28-2x. List the sides of <>ABC in order from shortest to longest.
Answers: a. AB;AC;BC b. BC;AB;AC
c. AC;AB;BC d. AB;BC;AC
You know the angles add to 180
so add them up and solve for x.
9x-7 + 7x-9 + 28-2x=180
solve for x.
That will give you the angles. Then, the longest side is opposite the larger angle, and so on.
i got x=11 but the sum of the sides equal 166 and not 180 what did i do wrong??
To solve for x and find the correct lengths of the sides, let's go through the steps again.
We have the angles:
m<A = 9x - 7
m<B = 7x - 9
m<C = 28 - 2x
To find x, let's set up the equation by summing up the angles and equating them to 180:
(9x - 7) + (7x - 9) + (28 - 2x) = 180
Now simplify and solve for x:
16x + 12 = 180
16x = 168
x = 10.5
So, it looks like you made an error in solving for x. The correct value is x = 10.5, not 11.
Now let's substitute this value back into the angles to find their values:
m<A = 9(10.5) - 7 = 94.5 - 7 = 87.5
m<B = 7(10.5) - 9 = 73.5 - 9 = 64.5
m<C = 28 - 2(10.5) = 28 - 21 = 7
Now that we have the angles, we can determine the sides of the triangle.
The longest side is opposite the largest angle, so side AC is the longest side.
The shortest side is opposite the smallest angle, so side BC is the shortest side.
Therefore, the sides of <>ABC in order from shortest to longest are:
BC, AB, AC
Hence, the correct answer is option d. AB; BC; AC.