On a map, richmond, danville, and charlottesville form a triangle. charlottesville is 85 miles from richmond and danville is 100 miles from richmond. which is a possible distance between danville and charlottesville?

The rest of the question is the options of the
A) 5 miles
B) 15 miles
C) 150 miles
D) 185 miles

Solution:


In any triangle, the sum of two any sides must be greater than the remaining side.
Richmond, Danville, and Charlottesville form a triangle
The sides of this triangle are 85 , 100  and x
x must be one of the given options 
So, we will check each option to find the correct answer

if x = 5 miles     ⇒⇒⇒ ∴ 5 + 85 = 90 (<) 100    ⇒⇒ wrong option

if x = 15 miles   ⇒⇒⇒ ∴ 15 + 85 = 100 (=) 100 ⇒⇒Wrong option

if x = 150 miles ⇒⇒⇒ ∴ 100 + 150 = 250 (>) 85
                                    &  100 + 85 = 185 (>) 150
                                    &  150 + 85 = 253 (>) 100 ⇒⇒⇒ correct option

if x = 185 miles ⇒⇒⇒ ∴ 100 + 85 = 185 (=) 185 ⇒⇒⇒ wrong option

∴ The possible distance between Danville and Charlottesville is 150 miles

The correct answer is option C) 150 miles