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? *

3 : 2

5 : 4

5:7

4:5

GUYS PLEASE TELL ME THE CORRECT ANSWER QUICKLY...​

Answer 1

Answer:

4:5

Step-by-step explanation:

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

and

Area(△DEF)

Area(△ABC)

=

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)

=

DM

2

AL

2

⇒

25

16

=

DM

2

AL

2

[Using (i)]

⇒

DM

AL

=

5

4

Hence, AL:DM=4:5

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