Question

Two isosceles triangles have equal
angles and their areas are in the ratio
16:25. Find the ratio of their
corresponding heights. दो समद्विबाहु
त्रिभुजों, जिसमें दो कोण बराबर है, के क्षेत्रफलों
का अनुपात 16:25 है। इन त्रिभुजों की संगत
उंचाईओं का अनुपात क्या है? *​

Answer 1

Answer:

Step-by-step explanation:

Here is your ANSWER

Let △ABC and △DEF be the given triangles such that AB=AC and DE=DF, ∠A=∠D

and

Area(△DEF)

Area(△ABC)

there ratios = 25/16

​

.......(i)

Draw AL⊥BC and DM⊥EF.

Now, AB=AC,DE=DF

⇒

AC / AB = 1

​ and ,

DF / DE = 1

​

⇒

AC / AB = DF DE

​

DE / AB = DF / AC

​

Thus, in triangles ABC and DEF, we have

DE / AB = DF / AC

​

AND ∠A=∠D [Given]

So, by SAS-similarity criterion, we have

△ABC∼△DEF

⇒

Area(△DEF)

Area(△ABC)

​

= 1/ 2 × DM = 16 / 25

1/ 2 × AL

​

=

DM

2

AL

2

​

[Using (i)]

⇒

DM

AL

​

=

5

4

​

Hence, AL:DM=4:5

Answer 2

Answer:

Two isosceles triangles have equal angles and their areas are in the ratio 16 : 25. Find the ratio of their corresponding heights. दो समद्विबाहु त्रिभुजों, जिसमें दो कोण बराबर है, के क्षेत्रफलों का अनुपात 16:25 है। इन त्रिभुजों की संगत उंचाईओं का अनुपात क्या है? *

3 : 2

5 : 4

5:7

4:5