Question

2Two sides of a triangle measure 16 inches and 10 inches. Which CANNOT be the

length of the remaining side?
A 6 in.
B 8 in.
C 14 in.
D 21 in.

Answer 1

Answer: A 6 in.

Explanation:

a=16 inches b=10 inches

Let the angle between these two sides is θ>0

Hence cosθ<1

Thus,

`The\ remaining \ side\ = \ √(a^2+b^2-2abcos\theta)\\\\ The\ remaining \ side\ > \ √(16^2+10^2-2(16)(10)(1)) \\\\The\ remaining \ side\ > \ √(256+100-320) \\\\The\ remaining \ side\ > \ √(356-320)\\\\The\ remaining \ side\ > \ √(36) \\\\The\ remaining \ side\ > \ 6\ inches`