Prove which divide these sides in the ratio 2: 1, Mathematics

Assignment Help:

In a right triangle ABC, right angled at C, P and Q are points of the sides CA and CB respectively, which divide these sides in the ratio 2: 1. Prove that 

9AQ2= 9AC2 +4BC2

9BP2= 9BC2 + 4AC2

9 (AQ2+BP2) = 13AB2

1904_right triangle.png

Ans:    Since P divides AC in the ratio 2 : 1

CP = 2/3 AC  QC = 2/3 BC

AQ2 = QC2 + AC2

AQ2 = 4/9  BC2 + AC2

9 AQ2 = 4 BC2  + 9AC              ...................... (1)

Similarly we get 9 BP2 = 9BC2 + 4AC2 ....................(2)

Adding (1) and (2) we get 9(AQ2 + BP2) = 13AB2


Related Discussions:- Prove which divide these sides in the ratio 2: 1

How much area will it irrigate in 30 minutes , Water in a canal 30 dm wide ...

Water in a canal 30 dm wide and 12 dm deep is flowing with a velocity of 10 km/h. How much area will it irrigate in 30 minutes if 8 cm of standing water is required for irrigation?

Angles of elevation and depression, Can someone please help me grasp the co...

Can someone please help me grasp the concept of angles of depression and elevation?

Vector function - three dimensional spaces, Vector Function The good wa...

Vector Function The good way to get an idea of what a vector function is and what its graph act like is to look at an instance.  Thus, consider the following vector function.

Determine the projection - vector, Determine the Projection of b = (2, 1, -...

Determine the Projection of b = (2, 1, -1) onto a = (1, 0, -2) There is a requirement of a dot product and the magnitude of a. a →  • b → = 4                             ||a

What is the percent of increase heating oil, The price of heating oil rose ...

The price of heating oil rose from $1.10 per gallon to $1.43 per gallon. What is the percent of increase? The price of heating oil rose $0.33 ($1.43 - $1.10 = $0.33). To ?nd ou

Find the volume of water left in the cylindrical tub, A solid is in the for...

A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 3.5 cm and the height of the cone is 4 cm. The solid is placed in a cylindr

Comperised payrolll package, a computerized payroll package and its cost,fu...

a computerized payroll package and its cost,futures and the size of the business and how business mathematics is an inbuilt component of the package

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd