Problema Solution
the perimeter of ΔABC is less than 98 centimeters but greater than 85 centimeters.
If side BC is a whole number of centimeters, what is the shortest length side BC may be?
Side AB is 31 cm, side AC is 36 cm, BC ? (these are the measurements of the triangle)
**this answer in the book is 19 cm. Please help me figure out how they got this answer?
Answer provided by our tutors
let BC the length of the shortest side and BC is integer
the perimeter P = AB + BC + AC = 31 + 36 + BC = 67 + BC
the perimeter of ΔABC is less than 98 centimeters but greater than 85 centimeters
85 < P < 98
85 < 67 + BC < 98 the inequality will not change if we subtract 67 on both sides
85 - 67 < 67 + BC - 67 < 98 - 67
18 < BC < 31
the smallest integer from the interval (18, 31) is 19 therefore the answer is 19 cm.