In a right △ABC, a perpendicular BD is drawn on to the largest side from the

Question

In a right

△

ABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does not give the ratio of the areas of

△

ABD and

△

ACB?

Options:

A . (ABAC)2

B . (ADAB)2

C . (BDCB)2

D . (ABAD)2

Answer: Option D
:
D
Consider ΔABD andΔACB:

∠BAD = ∠BAC [common angle]
∠BDA = ∠ABC [

90^{\circ}

]
By AA similarity criterion,

△ A B D ~ △

ACB
Hence,

\frac{a r (Δ A B D)}{a r (Δ A C B)} = ({\frac{A B}{A C})}^{2} = ({\frac{A D}{A B})}^{2} = ({\frac{B D}{C B})}^{2}

Was this answer helpful ?

Next Question

More Questions on This Topic :

Question 1. The ratio of the corresponding sides of two similar triangles is 1 : 3. The ratio of their corresponding heights is ____....: 3. The ratio of their corresponding heights is _________.

Question 2. In both the figures given below, all of the respective sides are equal and all interior angles are 90∘. Are the figur....interior angles are 90∘. Are the figures shown below similar?

Question 3. A farmer had three land plots as shown. He has to divide the plots equally among 2 of his sons. He gives Area a and Area....True if he has given equal area else enter false.

Question 4. In ΔABC, AB=BC=6cm. If a circle is drawn with center at B and radius 2 cm which intersects AB and BC at E and D, then ....intersects AB and BC at E and D, then ΔABC∼ΔEBD.

Question 5. In △ ABC, ∠A and ∠C are given, the number of triangles that can be constructed with ....triangles that can be constructed with this data is -

Question 6. △ABC is such thatAB=3 cm,BC=2 cm and CA=2.5 cm. △DEF is similar to △ABC. If EF=....△ABC. If EF=4 cm, then the perimeter of △DEF is ____.

Question 7. A ladder is resting on a wall of height 10√7m such that the foot of the ladder when placed 10√7m away fr....far is the foot of the ladder from the wall?

Question 8. Find the ratio of area of the equilateral triangles whose sides are 3 and 4 units.....

Question 9. ABCD is a square. Equilateral triangles ACF and ABE are drawn on the the diagonal AC and side AB respectively. Find area....AB respectively. Find area of △ACF : area of △ABE.

Question 10. In the adjoining figure, if BC=a,AC=b,AB=c and ∠CAB=120∘,then which of the following is the correct relation?....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0