Question 77

Let ABC be a right-angled triangle with hypotenuse BC of length 20 cm. If AP is perpendicular on BC, then the maximum possible length of AP, in cm, is

Name: Let ABC be a right-angled triangle with hypotenuse BC of length 20 cm. If AP is perpendicular on BC, then the maximum possible length of AP, in cm, is
Uploaded: May 3, 2022, 4:57 p.m.
Duration: 4 min 34 s
Description: Let ABC be a right-angled triangle with hypotenuse BC of length 20 cm. If AP is perpendicular on BC, then the maximum possible length of AP, in cm, is

Solution

Let p be the length of AP.

It is given that $$\angle\ BAC\ =90\ $$ and $$\angle\ APC\ =90\ $$

Let $$\angle\ ABC\ =\theta\ $$, then $$\angle\ BAP\ =90-\theta\ $$ and $$\angle\ BCA\ =90-\theta\ $$

So $$\angle\ PAC\ =\theta\ $$

Triangles BPA and APC are similar

$$p^2=x\left(20-x\right)$$

We have to maximize the value of p, which will be maximum when x=20-x

x=10

Share on Whatsapp Share on Whatsapp

Boost your CAT prep: Take All-India 3 free CAT mock tests with Video solutions

Video Solution

Click on the Email ☝️ to Watch the Video Solution

Create a FREE account and get:

All Quant CAT complete Formulas and shortcuts PDF
35+ CAT previous year papers with video solutions PDF
5000+ Topic-wise Previous year CAT Solved Questions for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Linear Equations Questions CAT Percentages Questions CAT Profit And Loss Questions CAT Probability, Combinatorics Questions CAT Time Speed Distance Questions

CAT DILR Questions | LRDI Questions For CAT

CAT DI with connected data sets Questions CAT Venn Diagrams Questions CAT Table with Missing values Questions CAT Puzzles Questions CAT Routes And Networks Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Para Jumbles Questions CAT Grammar and Sentence Correction Questions CAT Miscellaneous Questions CAT Critical Reasoning Questions CAT Vocabulary Questions

Let ABC be a right-angled triangle with hypotenuse BC of length 20 cm. If AP is perpendicular on BC, then the maximum possible length of AP, in cm, is

Video Solution

CAT Quant Questions | CAT Quantitative Ability

CAT DILR Questions | LRDI Questions For CAT

CAT Verbal Ability Questions | VARC Questions For CAT

Also Read

Related Formulas With Tests

CAT 2019 QA Slot 2 Question

Let ABC be a right-angled triangle with hypotenuse BC of length 20 cm. If AP is perpendicular on BC, then the maximum possible length of AP, in cm, is

Video Solution

CAT Quant Questions | CAT Quantitative Ability

CAT DILR Questions | LRDI Questions For CAT

CAT Verbal Ability Questions | VARC Questions For CAT

Also Read

Free CAT Quant Questions

Related Formulas With Tests

Login to your Cracku account

Hello! 👋

Ready to Unlock Your Success?

Please Enter Your OTP

Please enter the following details

Create a free Cracku account

Get Started with 5000+ Free CAT Questions & Mock Tests with Detailed Solutions!