ΔABC is right angled at B,BD is perpendicular to AC If AD a and CD b then ab2 is equal to

Solution:

From the right angled triangle ADC,

Using pythagoras theorem, AD2 + DC2 = AC2 --- (1)

From the figure,

DC = DB +BC --- (2)

Substitute DC from (2) in equation (1)

AD2 + (BD + BC)2 = AC2

AC2 = AD2 + BD2 + BC2 + 2BD.BC --- (3)

Also from right angled triangle ADB,

AD2 + BD2 = AB2 (From pythagoras theorem) --- (4)

Substitute (4) in equation (3)

AC2 = AB2 + BC2 + 2BD.BC

In the given figure, ΔABC is an obtuse triangle, obtuse angled at B. If AD⊥CB , then prove that AC2 = AB2 + BC2 + 2BC.BD ?

Summary:

Given ΔABC is an obtuse triangle, obtuse angled at B and AD⊥CB, then AC2 = AB2 + BC2 + 2BC.BD.

In the figure ABC is a right angled triangle with right angle at B. BD is perpendicular to AC. Then which of the following options will hold true?A. A B2=A D × D CB. AB 2= AD × ACC. AD 2= DC × ACD. A B2=D C2+A D2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Solution

The correct option is BAB2 = AD × ACIn △ABC and △ADB ∠ABC=∠ADB=90o ∠A=∠A (common angle) Therefore, △ABC∼△ADB by AA similarity ABAD=ACAB AB2=AC∗AD

Given,

∆ABC in which ∠B = 90° and BD ⊥ AC

Also, AD = 4 cm and CD = 5 cm

In ∆ADB and ∆CDB,

∠ADB = ∠CDB [each equal 90°]

∠BAD = ∠DBC [each equal to 90°-∠C]

∴ ∆DBA ∼ ∆DCB [by AAA similarity criteria]

Then,

In right angled ∆BDC,

BC2 = BD2 + CD2 [by Pythagoras theorem]

= BC2 = (2√5)2 + (5)2

= BC2 = 20 + 25 = 45

= BC = √45 = 3√5

Again,

Hence, BD = 2√5cm and AB = 6cm.

Triangle ABC is right angled at B and D is a point of BC such that BD = 5 cm, AD = 13 cm and AC = 37 cm, then find the length of DC in cm.

This question was previously asked in

SSC CGL 2020 Tier-I Official Paper 21 (Held On : 24 Aug 2021 Shift 3)

View all SSC CGL Papers >

1. 25
2. 35
3. 5
4. 30

Answer (Detailed Solution Below)

Option 4 : 30

Free

Electric charges and coulomb's law (Basic)

10 Questions 10 Marks 10 Mins

Given:

ΔABC is a right-angled triangle at B.

BD = 5 cm

AD = 13 cm

AC = 37 cm

Concept used:

If ΔABC is a right-angled triangle at B & AC is the hypotenuse, then according to Pythagoras theorem,

AB2 + BC2 = AC2

Calculation:

Here, ΔABD is also a right-angled triangle.

So,

AB2 + BD2 = AD2

⇒ AB2 = 169 - 25

⇒ AB = 12

We know,

AB2 + BC2 = AC2

⇒ BC2 = AC2 - AB2

⇒ BC2 = 372 - 122

⇒ BC = 35

⇒ BD + DC = 35

⇒ DC = 30

∴ The measure of DC is 30 cm.

Last updated on Sep 22, 2022

CDS I 2022 OTA SSB Selection Link Active Now! The OTA SSB Selection Link for SSCW (NT)-31 Course April 2023 is active till 3 pm 24th October 2022 and SSC (NT)-117 Course April 2023 is active till 10 am 25th October 2022.  Earlier, the Union Public Service Commission released the UPSC CDS II Result for the Written Examination. The CDS II 2022 exam was conducted on 4th September 2022. The candidates who are qualified in the written test are eligible to attend the Interview. A total number of 6658 candidates are shortlisted. The Interview Schedule will be released soon. This year a total number of 339 vacancies have been released for the UPSC CDS Recruitment 2022. The application process was conducted between 18th May 2022 and 7th June 2022.

Stay updated with the Quantitative Aptitude questions & answers with Testbook. Know more about Geometry and ace the concept of Triangles, Congruence and Similarity.