Question

The two isosceles
right-angle triangles
shown in the figure
are similar triangles.
If the ratio of the
area of the triangles
is 1:3, what is X in
cm?
36 cm​

Answer 1

Step-by-step explanation:

Bro pls Show the diagram Or attach it. If u attach the diagram I'll return and edit my answer!

Answer 2

Answer:

10th

Maths

Triangles

Criteria for Triangle Similarity

Two isosceles triangles hav...

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Asked on December 26, 2019 by

Roshna Varshney

Two isosceles triangles have equal vertical angles and their areas are in the ratio 9:16. Find the ratio of their corresponding heights.

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ANSWER

Let ABC,PQR be two isosceles triangle with equal vertical angles.

Let in ΔABC,AB=AC

⇒∠B=∠C=

2

180−∠A

And in ΔPQR,PQ=PR

⇒∠Q=∠R=

2

180−∠P

Given two vertical angles are equal.

∴∠A=∠P

⇒∠B=∠C=∠Q=∠R

By AAA postulate, "two triangles are similar if they have three corresponding angles congruent."

∴ΔABC∼ΔPQR

We know ratio between the areas of two similar triangles is same as the ration between the squares of their corresponding altitudes and corresponding heights of two given triangles are AD and PS.

AreaofΔPQR

AreaofΔABC

=

PS

2

AD

2

⇒

16

9

=

PS

2

AD

2

⇒AD:PS=3:4