Question

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?​

Answer 1

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,

$\frac{TV}{TS}=\frac{TW}{TU}\\\\ \frac{24}{TS}=\frac{21}{TU}\\\frac{TU}{TS}=\frac{7}{8}=k(say)$

Then, TU=7k and TS=8k

$\frac{TV}{TS}=\frac{VW}{SU}\\\\ \frac{24}{TS}=\frac{30}{SU}\\\frac{24}{8k}=\frac{30}{SU}\\SU=10k$

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