Question

The area of triangle ABC=144 squad. cm and area of triangle PQR=25 squad. cm Altitude of ABC=6cm.If triangle ABC congruent to PQR then the corresponding altitude of PQR is​

Answer 1

Correct Question :- The area of triangle ABC=144 squad. cm and area of triangle PQR=25 squad. cm Altitude of ABC=6cm.If triangle ABC similar to PQR then the corresponding altitude of PQR is ?

Given :-

• Area ∆ABC = 144 cm².
• Area ∆PQR = 25 cm².
• Altitude of ∆ABC = 6cm.
• ∆ABC ≅ ∆PQR.

To Find :-

• The corresponding Altitude of ∆PPQR ?

Concept used :-

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

Let us assume that ∆ABC is Similar to ∆PQR,

Than, we can say that :-

→ (Area ∆ABC) / (Area ∆PQR) = (AB/PQ)² = (BC/QR)² = (CA/RP)² = (Altitude of ∆ABC / Altitude of ∆PQR)²

Solution :-

By above told concept we get,

→ (Area ∆ABC) / (Area ∆PQR) = (Altitude of ∆ABC / Altitude of ∆PQR)²

Putting values Now, we get,

→ 144/25 = (6 / Altitude of ∆PQR)²

→ (12/5)² = (6 / Altitude of ∆PQR)²

Square root Both sides Now,

→ (12/5) = (6 / Altitude of ∆PQR)

→ 12 * Altitude of ∆PQR = 6 * 5

Divide both sides by 6,

→ 2 * Altitude of ∆PQR = 5

→ Altitude of ∆PQR = (5/2) = 2.5 cm. (Ans.)

Hence, The corresponding Altitude of ∆PPQR is 2.5cm.

Answer 2

Answer:

a) 2.5cm

b) 5cm

c) 12cm

d) 6cm

The answer for this question is a) 2.5cm

is the correct answer

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