2020Q6(b)(iii)Similarity (With Applications to Maps and Models)

NumericalEasy1 mark

6(b)

In the given figure AB = 9 cm, PA = 7.5 cm and PC = 5 cm. [3] Chords AD and BC intersect at P.

Find area of ΔPAB: area of ΔPCD

Topic: Similarity / area ratio

Previous-year question practice database

Answer

Exam answer

From ΔPAB ∼ ΔPCD:

AP/PC = 7.5/5 = 3/2

For similar triangles:

Area(ΔPAB) / Area(ΔPCD) = (AP/PC)²

= (3/2)²

= 9/4

Therefore:

Area(ΔPAB) : Area(ΔPCD) = 9 : 4

Answer:

9 : 4.

Explanation

For similar triangles, the ratio of their areas is the square of the ratio of any pair of corresponding sides. Here AP : PC = 7.5 : 5 = 3 : 2, so the area ratio is 3² : 2² = 9 : 4.

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