PROBLEM OF THE WEEK 3

Problem of the Week 2 Update

Two correct solutions were received. Congratulations to Mr. Isaiah Duazo an ECE student of Rizal Technological University and Mr. Jobert Gimeno an ECE student of PUP Sta. Mesa for submitting the correct solutions.

Solution by Isaiah Duazo:

tan A = 22/7
let A is equal to B + D
tan A = TAn (B + D)
(1) Tan (B + D) = (Tan B + Tan D)/[1 - (TAn B)(Tan D)]

Let the length of the altitude be h:

Tan B = 3/h
TAn D = 17/h

Substituting the value of Tan A, Tan B, and Tan D to Equation 1 and solving for h:

h = 11 units

Area of triangle = (base)(height)/2 = (20)(11)/2 = 110 square units

Problem of the Week 1 Update

No correct solutions were received.

PROBLEM OF THE WEEK 2

In the triangle ABC, the foot of the perpendicular from A divides the opposite side into parts length 3 and 17, and tan A = 22/7. Find the area of triangle ABC.

PROBLEM OF THE WEEK 1

Welcome to Math Challenges

Welcome to the newly created website Math Challenges. This site will post math problems weekly for you to answer. You can send your answer via electronic mail at mlzarco@engineer.com or by posting your answer here. This can be done by requesting to be a member of mathchallenges.blogspot.com. Feel free to email me on the above address for any questions or inquiries. Thanks and have fun doing mathematics.