The perimeter of a triangle is 56 inches. The second side is 2 inches more than twice the first side, and the third side is 18 inches less than three times the first side. Find the lengths of the three sides.

A) 10 inches, 22 inches, 24 inches
B) 12 inches, 26 inches, 20 inches
C) 14 inches, 28 inches, 22 inches
D) 16 inches, 30 inches, 18 inches

The lengths of the sides of the triangle are solved using algebra, giving results of 12 inches, 26 inches, and 18 inches, matching option B with a minor numerical discrepancy in the question's options.

Explanation:

The perimeter of a triangle is 56 inches, and we have two conditions for the sides of the triangle: the second side is 2 inches more than twice the first side, and the third side is 18 inches less than three times the first side. Let's use algebra to solve this:

Let the first side be represented by x inches.
The second side then is 2x + 2 inches, according to the problem statement.
The third side is 3x - 18 inches.
The total perimeter is the sum of all sides, which equals 56 inches. So, we have the equation x + (2x + 2) + (3x - 18) = 56.
Simplifying this equation, we get 6x - 16 = 56, which simplifies further to 6x = 72.
Dividing both sides by 6 gives us x = 12 inches.
Substituting x = 12 inches back into the equations for the second and third sides, we get the second side as 26 inches and the third side as 18 inches.

Therefore, the lengths of the three sides of the triangle are 12 inches, 26 inches, and 18 inches, which corresponds to option B.) 12 inches, 26 inches, 20 inches.

nareenasad80 nareenasad80 · Answer 2 · 2023-12-04T17:51:51-05:00

Answer:

The correct answer is option D) 12 inches, 26 inches, 18 inches.

Step-by-step explanation:

To solve this problem, let's denote the lengths of the sides of the triangle as follows:

Let x represent the length of the first side.
The second side is 2 inches more than twice the first side, so its length is 2x+2.

The third side is 18 inches less than three times the first side, so its length is 3x−18.

According to the perimeter formula for a triangle, the sum of the lengths of its three sides is equal to the perimeter, which is 56 inches.

So, we can write the equation:

x+(2x+2)+(3x−18)=56

Now, let's solve for x:

x+2x+2+3x−18=56

6x−16=56

6x=56+16

6x=72

x=72/6

x=12

Now, we have found the length of the first side: x=12 inches.

To find the lengths of the other two sides, we substitute x=12 into the expressions we derived earlier:

Length of the second side: 2x+2 = 2(12)+2 = 26 inches.
Length of the third side: 3x−18 = 3(12)−18 = 36−18 = 18 inches.