Answer:
38.9 cm²
Explanation:
You want the area of triangle ABC, given that AC = 7 cm, BC +AB = 28 cm, and BC -AB = 4 cm.
Side lengths
The sum and difference values can be used to find AB and BC:
BC +AB = 28
BC -AB = 4
Adding these equations gives ...
2BC = 32
BC = 16
Then AB is ...
AB = BC -4 = 12
Area
The area of the triangle can be found using Heron's formula:
A = √(s(s -a)(s -b)(s -c)) . . . . . where s = (AB +BC +AC)/2
s = (12 +16 +7)/2 = 35/2 = 17.5
A = √(17.5(17.5 -16)(17.5 -7)(17.5 -12)) = √(17.5·1.5·10.5·5.5)
A = √1515.9375 ≈ 38.935
The area of the triangle is about 38.9 square centimeters.