AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

State true or false.
The areas of similar triangles have the same ratio as the squares of the corresponding altitudes.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

△ ABC is similar to △ DEF

AX and DY are altitudes drawn in

△ ABC

and

△ DEF

respectively.
Question Image

Now, in

△ AXB

and

△ DEY,

∠ AXB = ∠ DYE = 90^{\circ}

(provided)

∠ B = ∠ E

(since, △ ABC

\sim △ DEF)

∴ ∠ BAX = ∠ EDY

….. (Third angle)
So, by similarity rule,

∠ ABX

\sim ∠ DEY

Thus, by ratio- side property of similar triangle,

\Rightarrow \frac{AB}{DE} = \frac{AX}{DY}

As,

△ ABC

is similar to

△ DEF

The ratios of area of both triangles can be given as,

\begin{matrix} \frac{ar △ ABC}{ar △ PQR} = \frac{\frac{1}{2} \times BC \times AX}{\frac{1}{2} \times EF \times DY} \\ \frac{ar △ ABC}{ar △ PQR} = \frac{BC \times AX}{EY \times DY} \end{matrix}

Thus, for similar triangles,

\frac{Area of △ ABC}{Area of △ DEF} = \frac{{AB}^{2}}{{DE}^{2}}

Also,

\frac{ar △ ABC}{ar △ DEF} = {(\frac{AB}{DE})}^{2} = {(\frac{BC}{EF})}^{2} = {(\frac{CA}{DF})}^{2}

Thus, the ratio of area of both will be equal to the ratio of squares of corresponding sides.
Correct option is 1.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!