The perimeter of a triangle is 30cm. If two of the sides are 13cm and 11cm, what is the length of the third side?
A. 6cm
B. 12cm
C. 15cm
D. 18cm
E. 22cm
Answer (2)
The length of the third side of the triangle is 6 cm, based on the perimeter of 30 cm and the two known sides of 13 cm and 11 cm. The calculation is done by rearranging the perimeter formula. Therefore, the chosen option is A, 6 cm.
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Define the sides of the triangle as a , b , and c , and the perimeter as P .
Substitute the given values a = 13 cm, b = 11 cm, and P = 30 cm into the perimeter formula P = a + b + c .
Solve for the unknown side c by rearranging the formula: c = P − a − b .
Calculate the length of the third side: c = 30 − 13 − 11 = 6 cm. The length of the third side is 6 .
Explanation
Problem Analysis We are given that the perimeter of a triangle is 30cm, and two of its sides are 13cm and 11cm. We need to find the length of the third side.
Define Variables and Formulas Let the sides of the triangle be a , b , and c . We are given that a = 13 cm, b = 11 cm, and the perimeter P = 30 cm. The formula for the perimeter of a triangle is P = a + b + c .
Substitution Substitute the given values into the formula: 30 = 13 + 11 + c .
Isolate the Unknown Solve for c : c = 30 − 13 − 11 .
Calculation Calculate the value of c : c = 30 − 24 = 6 cm.
Final Answer Therefore, the length of the third side is 6 cm.
Examples
Understanding how to calculate the side length of a triangle given its perimeter and the lengths of the other two sides is useful in various real-world scenarios. For example, if you are building a triangular frame for a painting and know the total length of wood you have and the lengths of two sides, you can calculate the length of the third side to ensure the frame fits together perfectly. This concept is also applicable in construction, carpentry, and even in creating geometric designs.
