Answer:
101.4 units²
Step-by-step explanation:
If RT = 12 and TU = 5 then
⇒ RU = RT + TU
= 12 + 5
= 17 units
If RS is 7 more than RU then
⇒ RS = RU + 7
= 17 + 2
= 24 units
The ΔRSU is a right triangle with the right angle at ∠RUS.
Therefore, use Pythagoras' Theorem to find SU:
⇒ RU² + SU² = RS²
⇒ 17² + SU² = 24²
⇒ SU² = 24² - 17²
⇒ SU² = 287
⇒ SU = √287 units
Area of ΔRST = 1/2 × base × height
= 1/2 × 12 × √287
= 101.6464461... units²
(Please note: The answer quoted above is accurate. The answer given in the answer options uses the rounded value of SU to 1 decimal place).
