Mathematics
Angle BAC of triangle ABC is obtuse and AB = AC. P is a point in BC such that PC = 12 cm. PQ and PR are perpendiculars to sides AB and AC respectively. If PQ = 15 cm and PR = 9 cm; find the length of PB.
Similarity
7 Likes
Answer
In ΔABC,
AC = AB [Given]
So, ∠ABC = ∠ACB [Angles opposite to equal sides are equal.]
In ΔPRC and ΔPQB,
∠RCP = ∠QBP [As ∠ABC = ∠ACB]
∠PRC = ∠PQB [Both are right angles.]
Hence, ∆PRC ~ ∆PQB [By AA]
Since, corresponding sides of similar triangles are proportional we have :
Hence, PB = 20 cm.
Answered By
5 Likes
Related Questions
In the given figure, ABC is a right angled triangle with ∠BAC = 90°.
(i) Prove that : △ADB ~ △CDA.
(ii) If BD = 18 cm and CD = 8 cm, find AD.
(iii) Find the ratio of the area of △ADB is to area of △CDA.
ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC. Prove that :
(i) △ADE ~ △ACB
(ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.
(iii) Find, area of △ADE : area of quadrilateral BCED.
Given : AB || DE and BC || EF. Prove that :
(i)
(ii) △DFG ~ △ACG.
PQR is a triangle. S is a point on the side QR of △PQR such that ∠PSR = ∠QPR. Given QP = 8 cm, PR = 6 cm and SR = 3 cm.
(i) Prove △PQR ~ △SPR.
(ii) Find the lengths of QR and PS.
(iii)
