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?
In an equilateral triangle, all three sides are equal in length.
So, to find the measure of the third side, we can set the two given sides equal to each other and solve for x:
3x + 15 = 7x - 5
Subtracting 3x from both sides:
15 = 4x - 5
Adding 5 to both sides:
20 = 4x
Dividing both sides by 4:
5 = x
Now that we have found the value of x, we can substitute it back into one of the expressions to find the length of the third side.
Let's use the first side expression:
3x + 15
Substituting x = 5:
3(5) + 15 = 30
So, the measure of the third side is 30 inches.