CBSE Class 10CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution for Two Isosceles Triangles Have Equal Vertical Angles and Their Areas Are in the Ratio 36 : 25. Find the Ratio of Their Corresponding Heights. - CBSE Class 10 - Mathematics

Login
Create free account


      Forgot password?

Question

Two isosceles triangles have equal vertical angles and their areas are in the ratio 36 : 25. Find the ratio of their corresponding heights.

Solution

Given: AB = AC, PQ = PQ and ∠A = ∠P

And, AD and PS are altitudes

And, `("Area"(triangleABC))/("Area"(trianglePQR))=36/25`                  .........(i)

To find `"AD"/"PS"`

Proof: Since, AB = AC and PQ = PR

Then, `"AB"/"AC"=1` and `"PQ"/"PR"=1`

`therefore"AB"/"AC"="PQ"/"PR"`

`rArr"AB"/"PQ"="AC"/"PR"`                ........(ii)

In ΔABC and ΔPQR

∠A = ∠P                                        [Given]

`"AB"/"PQ"="AC"/"PR"`                 [From (2)]

Then, ΔABC ~ ΔPQR                     [By SAS similarity]

`therefore("Area"(triangleABC))/("Area"(trianglePQR))="AB"^2/"PQ"^2`            .....(iii) [By area of similar triangle theorem]

Compare equation (i) and (iii)

`"AB"^2/"PQ"^2=36/25`

`"AB"/"PQ"=6/5`                 ..........(iv)

In ΔABD and ΔPQS

∠B = ∠Q                          [ΔABC ~ ΔPQR]

∠ADB = ∠PSQ                  [Each 90°]

Then, ΔABD ~ ΔPQS         [By AA similarity]

`therefore"AB"/"PQ"="AD"/"PS"`

`rArr6/5="AD"/"PS"`              [From (iv)]

  Is there an error in this question or solution?

APPEARS IN

Video TutorialsVIEW ALL [1]

Solution for question: Two Isosceles Triangles Have Equal Vertical Angles and Their Areas Are in the Ratio 36 : 25. Find the Ratio of Their Corresponding Heights. concept: Areas of Similar Triangles. For the course CBSE
S
View in app×