Area of a triangle | PRMO 2017 | Question 25

Try this beautiful problem from the Pre-RMO, 2017, Question 25, based on Area of a triangle.

Area of triangles - PRMO 2017, Question 25

Let ABCD be a rectangle and let E and F be points on CD and BC respectively such that area (ADE) =16, area (CEF) =9, and area (ABF) =25. What is the area of triangle AEF?

is 107
is 30
is 840
cannot be determined from the given information

Key Concepts

Equation

Algebra

Integers

Check the Answer

Answer: is 30.

PRMO, 2017, Question 25

Higher Algebra by Hall and Knight

Try with Hints

Let x=AD, a=DE, y-a=EC, b=FC, x-b=FB, y=AB

$xa=32, b(y-a) =18, y(x-b) =50$

or, $by-\frac{32b}{x}=18$

or, $b=\frac{18b}{xy-32}$

Area of a triangle problem

or, $xy-\frac{18xy}{xy-32}=50$

or, $xy=t$

or, $\frac{t^{2}-32t-18t}{t-32}=50$

or, $t^{2}-50t=50t-1600$

or, $t^{2}-100t+1600=0$

or, t=80,20

or, xy=80

or, area of triangle AEF= 80-(16+9+25)=30.

Other useful links

Related

Try this beautiful problem from the Pre-RMO, 2017, Question 25, based on Area of a triangle.

Area of triangles - PRMO 2017, Question 25

Let ABCD be a rectangle and let E and F be points on CD and BC respectively such that area (ADE) =16, area (CEF) =9, and area (ABF) =25. What is the area of triangle AEF?

is 107
is 30
is 840
cannot be determined from the given information

Key Concepts

Equation

Algebra

Integers

Check the Answer

Answer: is 30.

PRMO, 2017, Question 25

Higher Algebra by Hall and Knight

Try with Hints

Let x=AD, a=DE, y-a=EC, b=FC, x-b=FB, y=AB

$xa=32, b(y-a) =18, y(x-b) =50$

or, $by-\frac{32b}{x}=18$

or, $b=\frac{18b}{xy-32}$

Area of a triangle problem

or, $xy-\frac{18xy}{xy-32}=50$

or, $xy=t$

or, $\frac{t^{2}-32t-18t}{t-32}=50$

or, $t^{2}-50t=50t-1600$

or, $t^{2}-100t+1600=0$

or, t=80,20

or, xy=80

or, area of triangle AEF= 80-(16+9+25)=30.

Other useful links

Related

Leave a ReplyCancel reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy

Cheenta Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.

HALL OF FAME BLOG OFFLINE CLASS

CHEENTA ON DEMAND BOSE OLYMPIAD

Cheenta Academy Private Limited |

support@cheenta.com

Menu

Math Olympiad Program