1) If the perimeter of triangle STU is 125 cm, and segments TW, VW, and VT measure 21 cm, 30 cm, and 24 cm, respectively, what is the length of segment SU?

Question

asked Aug 10, 2022 54.1k views

1 Answer

Janaka R Rajapaksha · Answer 1 · 2022-08-14T02:18:22+0000

GIVEN: The perimeter of triangle STU is 125.

The segments TW=21 cm

VW=30 cm

VT=24 cm

TO FIND: The length of the segment SU.

SOLUTION:

As corresponding sides must be same. so we have,

$(TV)/(TS)=(TW)/(TU)\\\\ (24)/(TS)=(21)/(TU)\\(TU)/(TS)=(7)/(8)=k(say)\\$

Then, TU=7k and TS=8k

$(TV)/(TS)=(VW)/(SU)\\\\ (24)/(TS)=(30)/(SU)\\(24)/(8k)=(30)/(SU)\\SU=10k$

As the perimeter of triangle STU is 125.

so,

8·k+7·k+10·k=125

⇒25.k=125

⇒k=5

Therefore, SU=10×5=50