Find the value of c in a triangle, if the semi perimeter is 13cm and the values of a and b are 8cm and 7cm respectively.
Perimeter is the sum of all the sides of a triangle. The semi perimeter is half of the sum of all the sides of a triangle.
Answer: If the semi perimeter is 13 cm and the values of a and b are 8 cm and 7cm respectively, then the value of c in a triangle is 11cm.
Let us solve this step by step.
Let S be the semi perimeter of the triangle
Perimeter (P) of the triangle is twice the semi perimeter (S)
Given: S = 13 cm
P = 2S
= 2 ✕ 13
We know that Perimeter of the triangle is sum of the three sides.
P = a + b + c
26 = 8 + 7 + c
26 = 15 + c
⇒ c = 26 - 15
⇒ c = 11 cm