In the diagram, $\triangle P Q R$ has side lengths as shown. If $x=10$, the perimeter of $\triangle P Q R$ is
(A) 29
(B) 31
(C) 25
(D) 27
(E) 23
Solution 1

Since the side lengths of the triangle are $x-1, x+1$ and 7 , its perimeter is $(x-1)+(x+1)+7$ which equals $2 x+7$.

Since $x=10$, the perimeter equals $2 \times 10+7$ which is equal to 27 .

## Solution 2

Since $x=10$, the side lengths of the triangle are $x-1=9$ and $x+1=11$ and 7 .

The perimeter of the triangle is thus $9+11+7$ which equals 27 .

ANSWER: (D)