Question

20. Isosceles ∆QRS has dimensions QR=QS=60 and RS=30. The centroid of ∆QRS is located at point T. What is the distance from T to QR?

Answer 1

it has given that, Isosceles ∆QRS has dimensions QR = QS = 60 and RS = 30. The centroid of ∆QRS is located at point T.

To find : The distance from T to QR.

solution : we know, centroid is the intersection of medians of triangle. for isosceles triangle, median is also an altitude.

The median from Q to RS is also altitude to RS.

so, using Pythagoras theorem,

median = altitude = √{QR² - (RS/2)²}

= √{60² - 15²}

= √{3600 - 225}

= 15√15

we know, The centroid lies 2/3 of the way along median. so, distance of T from RS = 1/3 × 15√15 = 5√15.

here, ∆QRT , ∆RST and ∆SQT are all equal in area.

so, ar∆QRT = 1/2 × h × QR = ar∆RST

⇒1/2 × h × 60 = 1/2 × RS × distance from T to RS

⇒h × 30 = 1/2 × 30 × 5√15

⇒h = (5/2)√15 unit

Therefore the distance from T to QR is (5/2)√15 units.