The measures of two of the sides of an equilateral triangle are 3x + 15 in. and 7x – 5 in. What is the measure of the third side in inches? step by step
Responses
5
1
18
30
To find the measure of the third side of the equilateral triangle, we need to set the two given side lengths equal to each other and solve for x.
Given: 3x + 15 = 7x - 5
First, let's simplify the equation by combining like terms:
15 + 5 = 7x - 3x
20 = 4x
Next, divide both sides of the equation by 4 to solve for x:
20/4 = 4x/4
5 = x
Now that we have found the value of x, we can substitute it back into one of the given side lengths to find the measure of the third side:
3(5) + 15 = 30 + 15 = 45
Therefore, the measure of the third side is 45 inches. The correct answer is option 4.
the answer is 30 not 45
Apologies for the mistake. Let's go through the steps again to find the correct answer.
Given: 3x + 15 = 7x - 5
Simplifying the equation:
15 + 5 = 7x - 3x
20 = 4x
Divide both sides of the equation by 4 to solve for x:
20/4 = 4x/4
5 = x
Substitute x = 5 back into one of the given side lengths to find the measure of the third side:
3(5) + 15 = 30 + 15 = 45
Therefore, the measure of the third side is indeed 30 inches. The correct answer is option 3.
To find the measure of the third side of the equilateral triangle, we need to set up an equation.
Step 1: Given that two sides of the equilateral triangle have measures of (3x + 15) in. and (7x - 5) in., we can set up the equation:
(3x + 15) = (7x - 5)
Step 2: Simplify the equation by combining like terms:
3x + 15 = 7x - 5
Step 3: To isolate the variable, we can subtract 3x from both sides of the equation:
15 = 4x - 5
Step 4: Add 5 to both sides of the equation to further isolate the variable:
20 = 4x
Step 5: Divide both sides of the equation by 4 to solve for x:
x = 20/4
x = 5
Step 6: Now that we have found the value of x, we can substitute it back into one of the expressions for the sides of the triangle to find the measure of the third side. Let's use the expression (3x + 15):
Third side = (3x + 15) = (3 * 5 + 15) = (15 + 15)
Step 7: Simplify the expression to get the final answer:
Third side = 30 inches
Therefore, the measure of the third side of the equilateral triangle is 30 inches.
To find the measure of the third side of an equilateral triangle, we need to set up an equation using the given information.
Step 1: Assign variables to the given measures of the sides
Let's call the measure of the first side "a" and the measure of the second side "b."
Given:
The measure of the first side = 3x + 15 in.
The measure of the second side = 7x – 5 in.
So, we have:
a = 3x + 15
b = 7x – 5
Step 2: Use the fact that an equilateral triangle has all sides equal in length
In an equilateral triangle, all sides are equal. Therefore, the measure of the third side should also be equal to the measures of the first and second sides.
So, we can set up an equation:
a = b = 3rd side
Step 3: Substitute the variables with their given values
Since we know the values of a and b, we can substitute them into the equation:
3x + 15 = 7x – 5
Step 4: Solve for x
To solve the equation, we need to isolate the variable x on one side of the equation. Let's do that:
3x - 7x = -5 - 15
-4x = -20
x = (-20)/(-4)
x = 5
Step 5: Substitute the value of x back into the equation to find the measure of the third side
Now that we have the value of x, we can substitute it back into the equation to find the measure of the third side:
3rd side = a = 3x + 15
= 3(5) + 15
= 30
So, the measure of the third side of the equilateral triangle is 30 inches.