急! 有關三角形面積比計法 ?

(b)
The method used is:
"For a pair of similar triangles, the ratio of their areas is equal to theratio of the squares of the corresponding sides."

In the question, ΔPQT ~ ΔRST
Hence, the corresponding sides are in equal ratios, i.e.
PQ/RS = QT/ST = PT/RT

Applying the above method :
(Area of ΔPQT)/(Area of ΔRST) = (PQ/RS)² = (QT/ST)² = (PT/RT)²


(c)
ΔPST and ΔRST are not similar, and thus the method in (b) CANNOT be applied.

However, ΔPST and ΔRST have the bases PT and RT respectively, and both of them havethe same altitude (height) from S to their bases.
Let h be the altitude from S to the bases in both ΔPST and ΔRST.

Applying formula: (Area of triangle) = (1/2)x base x altitude
Area of ΔPST = (1/2) x PT x h ...... [1]
Arae of ΔRST = (1/2) x RT x h ...... [2]

[1]/[2]: (Area of ΔPST)/(Area of ΔRST) = PT/RT

In Part (a): ΔPQT ~ ΔRST
and thus: PQ/RS = QT/ST = PT/RT

Hence, (Area of ΔPST)/(Area of ΔRST) = PT/RT = QT/ST

多謝提醒。~~~~~~~~~~~~~~~~~~~~~

To Mr. Kwok :

(c)
題目沒有說 ST 是 ΔPST 的高，亦沒有說 ST 是 ΔRST 的高。
題目亦沒有足夠資料證明 ST 是這兩個三角形的高。

因此，應假設 ΔPST 和 ΔRST 的相同高為 SX。
Area of ΔPST = (1/2) x PT x SX
Arae of ΔRST = (1/2) x RT x SX