Chapter ISG, Problem 5.3.5P

a.

To determine

To find which side is shortest.

Answer to Problem 5.3.5P

Side a is shortest.

Explanation of Solution

Given information:

Triangular carpet

  

Side second is 2 ftlonger than a

Side third is 2 ftlonger than b

Maximum perimeter is 20 ft

Calculation:

Triangular carpet side one=a

Triangular carpet side second, b=a+2

Triangular carpet side third, c=b+2

Substituting value of b=a+2 in c

Then, c=a+4 As side a is shortest because side b is 2 ftlonger than a and side c is 4 ftlonger than a.

b.

To determine

To explain about shortest length.

Answer to Problem 5.3.5P

The shortest side will be less than or equal to

Explanation of Solution

Given information:

Triangular carpet

  

Side second is 2 ftlonger than a

Side third is 2 ftlonger than b

Maximum perimeter is 20 ft

Formula used:

Perimeter of triangle=a+b+c

Where a, b and c are sides of triangle

Calculation:

Triangular carpet side one=a

Triangular carpet side second, b=a+2

Triangular carpet side third, c=b+2

Substituting value of b=a+2 in c

Then, c=a+4 As side a is shortest because side b is 2 ftlonger than a and side c is 4 ftlonger than a.

Substituting the values of a, b and c in the formula

Perimeter of triangle=a+a+2+a+4=3a+6

As maximum perimeter=20 Inequality

  

Subtracting 6 both sides of inequality

  

On solving,

  

Dividing by 3 both sides of inequality

  

On solving,

  

Hence, the shortest side will be less than or equal to $\frac{14}{3}$ .