The perimeters of two similar triangles ∆ABC and ∆PQR are 35cm and 45cm respectively, then the ratio of the areas of the two triangles is

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

49:81

50:81

41:81

49:89

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given that perimeters of two similar triangles

Δ ABC and Δ PQR

are 35 cm and 45 cm.
The perimeter of two similar triangles ABC and PQR class 9 maths CBSE

We know that, the ratio of perimeters of two similar triangles is equal to the ratio of their corresponding sides.
Here,

Δ ABC ~ Δ PQR

.
Then,

AB PQ = BC QR = AC PR = Perimeter of ΔABC Perimeter of ΔPQR … … (1)

Substitute given perimeter values of two similar triangles

Δ ABC and Δ PQR

in eq (1).

AB PQ = BC QR = AC PR = 3545 AB PQ = BC QR = AC PR = 79 … … (2)

Apply Area of similar triangles theorem i.e., the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
substitute the value from eq(2).

ar Δ ABC ar Δ PQR = AB PQ 2 ar Δ ABC ar Δ PQR = 792 ar Δ ABC ar Δ PQR = 4981

Hence, the ratio of the areas of the two triangles is 49: 81.
The correct option is (1).

Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET