Question

the first side of a triangle measures 4 in. less than the second side, the third side is 3 in. more than the first side, and the perimeter is 15 in. How long is the third side?

Answer 1

Start by representing the lengths of the three sides of your triangle:

first side: x-4 (inches)
second side: x (inches)
third side: (x-4) + 3 (inches)

Add these three quantities up to obtain a formula for the perimeter, and set your sum equal to the given perimeter (15 inches):

x-4 + x + x-4 -3 = 15

3x-11=15
3x=26
x=26/3

Thus, the length of the 2nd side is 26/3; that of the first side is 26/3-4, or 14/3; and that of the third side is 14/3+3, or 23/3 (all measurements in inches).

Answer 2

The length of side 3 is 5.67 inches.

Explanation:

A triangle has three sides. The x represents the length of side 2.

• Side 1= x-4
• Side 2= x
• Side 3= x-4+3 = x-1

The total perimeter (P) of the triangle is 15.

P=S1+S2+S3

15=x-4+x+x-1

15=3x-5

15+5=3x

20=3x

20/3=x

x=6.67 (Length of side 2)

S3= x-1

S3=6.67-1

S3=5.67 inches

Check:

S1= x-4 = 6.67-4 = 2.67

S2= x=6.67

S3=x-4+3=x-1=5.67

P=S1+S2+S3

P=2.67+6.67+5.67

P=15