Answer:
The smallest possible perimeter of the triangle, rounded to the nearest tenth is 72.4 in
Step-by-step explanation:
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Let
x ------> the length of the remaining side
Applying the triangle inequality theorem
1) x+x > 30
2x > 30
x > 15 in
The perimeter is equal to
P=30+2x
<em>Verify each case</em>
1) For P=41.0 in
substitute in the formula of perimeter and solve for x
41.0=30+2x
2x=41.0-30
x=5.5 in
Is not a solution because the value of x must be greater than 15 inches
2) For P=51.2 in
substitute in the formula of perimeter and solve for x
51.2=30+2x
2x=51.2-30
x=10.6 in
Is not a solution because the value of x must be greater than 15 inches
3) For P=72.4 in
substitute in the formula of perimeter and solve for x
72.4=30+2x
2x=72.4-30
x=21.2 in
Could be a solution because the value of x is greater than 15 inches
4) For P=81.2 in
substitute in the formula of perimeter and solve for x
81.2=30+2x
2x=81.2-30
x=25.6 in
Could be a solution because the value of x is greater than 15 inches
therefore
The smallest possible perimeter of the triangle, rounded to the nearest tenth is 72.4 in
