Question

What are the lengths of SV and QT

Answer 1

QT=4x+1, SV = 9x-4

Explanation:

For QT:

1) segments RT and RV have the same length

2) segments QT and QV both start at point Q and end at opposite ends of segment TV which is perpendicular to segment QS

so the length of QV is equal to the length of QS

For SV:

1) segments RT and RV have the same length

2) segments ST and SV both start at point S and end at opposite ends of segment TV which is perpendicular to segment QS

so the length of SV is equal to the length of ST

Answer 2

Explanation:

it is a symmetric figure, because TR = RV, and TV and QS are perpendicular (90 degree angle).

therefore, all the triangles mirrored at SQ are similar triangles with scaling factor 1.

so, the missing sides are :

QT = QV = 4x + 1

SV = ST = 9x - 4