Question

In rhombus QRST,
TR = 6 and QS = 10.
Find TS.

Answer 1

`\sf C) √(34)`

Explanation:

In rhombus, the diagonals bisect each other at 90°.

∠TUS = 90° and

`\sf QU = SU = (1)/(2)*QS = (10)/(2) = 5 \ &\\\\\\TU = UR = (1)/(2)*TR=(6)/(2)=3`

In ΔTUS,

TU = 3

SU = 5 and ∠TUS = 90°

Use Pythagorean theorem to find TS,

`\sf TS^2 = TU^2 + SU^2`

`\sf = 3^2 + 5^2\\\\ = 9 + 25\\\\= 34`

`\sf \text{Take square root,}\\\\ \boxed{\bf TS = √(34)}`