MathDB

In the figure, AQPB and ASRC are squares, and AQS is an equilateral triangle. If QS = 4 and BC = x, what is the value of x? [asy] unitsize(16); pair A,B,C,P,Q,R,T; A=(3.4641016151377544, 2); B=(0, 0); C=(6.928203230275509, 0); P=(-1.9999999999999991, 3.464101615137755); Q=(1.4641016151377544, 5.464101615137754); R=(8.928203230275509, 3.4641016151377544); T=(5.464101615137754, 5.464101615137754); dot(A);dot(B);dot(C);dot(P); dot(Q);dot(R);dot(T); label("

A

", (3.4641016151377544, 2),E); label("

B

", (0, 0),S); label("

C

", (6.928203230275509, 0),S); label("

P

", (-1.9999999999999991, 3.464101615137755), W); label("

Q

", (1.4641016151377544, 5.464101615137754),N); label("

R

", (8.928203230275509, 3.4641016151377544),E); label("

S

", (5.464101615137754, 5.464101615137754),N); draw(B--C--A--B); draw(B--P--Q--A--B); draw(A--C--R--T--A); draw(Q--T--A--Q); label("

x

", (3.4641016151377544, 0), S); label("

4

", (Q+T)/2, N);[/asy]

4

Problems(1)