Question

The perimeter of a triangle is 70 feet. The length of the second side is 9 feet more than the first side. The third side is 1 foot longer than the first side. Model the situation with an equation and then solve to find the length of the shortest side.
PLEASE PROVIDE DETAILS

Answer 1

Answer:

Shortest side is 20 feet

All sides are 20, 21 and 29 feet

Step-by-step explanation:

Perimeter=a+b+c=70

where a, b & c are the sides of the triangle.

Now, b=a+9 .....given.... eqn 1

and c=a+1 .....given.... eqn 2

∴ a+b+c= a+(a+9)+(a+1)=70 .....  from eqn 1 and 2

a+a+9+a+1=70

3a+10=70

3a=60

a=20

Now, substituting this value in eqn 1 and 2,

b=a+9=20+9=29

c=a+1=20+1=21

Hence, the three sides of this triangle are 20, 21 and 29

CHECK

a+b+c=20+21+29=70