Question

$\large \pink{\underbrace{\bf{ \red{Solution}}}}$

___________________________
Two isosceles triangles have equal vertical angles and their areas in the ratio 25: 36. Find the ratio of their corresponding heights.
__________________________ Options:-
A-4:5
B-5:6
C-6:7
D-5:7
__________________________ Expecting answers from:-
=> Moderator(s)
=>Brainly Star(s)
=>Apprecentice moderator
=>Brainly Teacher(s)
=>Great User(s) ___________________________
No spam
Need answer with explanation​

Answer 1

Question:-

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

Options:

(A) 4:5.

(B) 5:6.

(C) 6:7.

(D) 5:7.

Given:-

AB = AC, PQ = PQ and ∠A = ∠P And, AD and PS are altitudes.

To Find:-

The ratio of the corresponding heights.

Solution:-

Then, ∆ABC ~ ∆PQR [By SAS Similarly]

$\sf \large \therefore \frac{Area (∆ABC)}{Area (∆PQR)} = \frac{AB {}^{2} }{PQ {}^{2} } \: \: ...(i)$

$\sf \large \frac{AB {}^{2} }{PQ {}^{2} } = \frac{25}{36}$

$\sf \large \frac{AB}{PQ} = \frac{5}{6}$

In ∆ABD & ∆PQS

∠B = ∠Q (∆ABC ~ ∆PQR)

∠ADB = ∠PSQ (Each 90°)

∆ABD ~ ∆PQS [By AA Similarly]

$\sf \large \therefore \frac{AB}{PQ} = \frac{AD}{ PS}$

$\sf \large \frac{5}{6} = \frac{AD }{ PS}$

$\sf \large = 5 :6$

Answer:-

${ \boxed{ \sf \large \color{red} \therefore The \: ratio \: of \: the \: corresponding \: heights = 5 \colon6.}}$

[Refer to to above attachment for diagram]

Hope you have satisfied. ⚘