Question

Geometry
Class 10

Guys help fast
No direct answer

Solve it properly with all steps

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Answer 1

Answer:

• 4 : 11 is the ratio of the areas of triangles.

Step-by-step explanation:

Given :

In ΔABC, P is a point on side BC such that BP = 4 cm and PC = 7 cm.

To find :

ar(ΔAPC) : ar(ΔABC) = ?

Solution :

Construction :

Draw AD⊥BC

• Finding area of ΔAPC:

⇒ 1/2 × base × height

⇒ 1/2 × BP × AD

⇒ 1/2 × 4 × AD

• Finding area of ΔABC:

⇒ 1/2 × base × height

⇒ 1/2 × BC × AD

⇒ 1/2 × 11 × AD

• Ratio of their areas:

⇒ [1/2 × 4 × AD]/[1/2 × 11 × AD]

⇒ [2 × AD]/[11/2 × AD]

⇒ 2 × 2/11

⇒ 4/11

∴ Ratio of ar(ΔAPC) : ar(ΔABC) is 4 : 11.