Mathematics
In the figure given below, AD ⊥ BC, AB = 25 cm, AC = 17 cm and AD = 15 cm. Find the length of BC.
Pythagoras Theorem
4 Likes
Answer
By pythagoras theorem,
In right angle triangle ADB,
⇒ AB2 = AD2 + BD2
⇒ 252 = 152 + BD2
⇒ 625 = 225 + BD2
⇒ BD2 = 625 - 225 = 400
⇒ BD = = 20 cm
In right angle triangle ADC,
⇒ AC2 = AD2 + DC2
⇒ 172 = 152 + DC2
⇒ 289 = 225 + DC2
⇒ DC2 = 289 - 225 = 64
⇒ DC = = 8 cm
From figure,
⇒ BC = BD + DC = 20 + 8 = 28 cm.
Hence, BC = 28 cm.
Answered By
3 Likes
Related Questions
In a right angled triangle ABC, right angled at C, P and Q are the points on the sides CA and CB respectively which divide these sides in the ratio 2 : 1. Prove that
(i) 9AQ2 = 9AC2 + 4BC2
(ii) 9BP2 = 9BC2 + 4AC2
(iii) 9(AQ2 + BP2) = 13AB2
In figure given below, triangle ABC is right angled at B. Given that AB = 9 cm, AC = 15 cm and D, E are mid-points of the sides AB and AC respectively, calculate (i) the length of BC (ii) the area of △ADE.
In the figure given below, ∠BAC = 90°, ADC = 90°, AD = 6 cm, CD = 8 cm and BC = 26 cm. Find
(i) AC
(ii) AB
(iii) area of the shaded region.
If in △ABC, AB > AC and AD ⊥ BC, prove that AB2 - AC2 = BD2 - CD2.