Triagle ABC is given. The side AB is decreased by $\frac{1}{4}$ of its length and side AC is increased by $\frac{1}{4}$ . The area of new triangle DCE is smaller than the original triangle by 2 $c{{m}^{2}}$ . Find the area of the original triangle ABC ?

Triangle ABC is given with AB = 9cm and the area is 36 cm^2. . Point M is on side BC, and BM = 3MC. A line is drawn through point M which intersects side AB at point K. The area of triangle KBM is also equal to 36 cm^2.  What is the length of side AK?

Triangle ABC is given with M is the midpoints of side AB is M, side MB is N, side AC is P and side PC is Q. Find the area of find the area of the quadrilateral MNQP if the area of the triangle ABC equals 16 cm².

Triangle ABC is given with point O lies inside the triangle. The area of the triangle AOB is 6 cm². The area of the triangle BOC is 8 cm². The area of the triangle COA is 2 cm².  The line OA splits the triangle ABC into two parts. Find the area of those two parts?

Triangle ABC is given. On side AB, take the points D and E so that AD = DE = EB. On the side AC, take the points M and N so that AM = MN = NC. Find the area of the triangle ABC. Knowing that the area of the quadrilateral DEMN is 6 cm² ?

The area of the triangle ABC is 420 cm². N is the midpoint edge CA. P is the point on the side AB; AP = 3 x PB. The line BN intersects CP at K. What is the area of the triangle BKC?

Quadrilateral ABCD is given. I is the midpoint of side AB. What is the area of the triangle ICD? Knowing the area of the triangles ACD is 12 $c{{m}^{2}}$ and BCD is 18 $c{{m}^{2}}$.

The area of quadrilateral ABCD is 34 cm². The line CB extends towards point B and the line DA extends towards point A, then the two lines intersect at point P. Find the area of triangles ABD and BCD? Knowing the area of the triangle PAB is  18 cm² and the area of triangle ABC is 6 cm².  

There are two types of car in the garage: 3-wheel car and 4-wheel car. The total number of cars is 40 and the total number of wheels is 148. How many cars are there for each type?

8^th of  March , 2004 is a Tuesday. 60 years later, on which day of the week was 8^th of March ?

( Monday, Tuesday, ……write as 2, 3, ….. )

The son’s present age is equal to $\frac{1}{2}$ of the difference between dad’s age and age of the son. 4 years ago, the son’s age is equal to $\frac{1}{3}$ of the difference between their ages. If the son’s age if $\frac{1}{4}$of the difference between their ages, how old is each of them?

A store has three oil tanks A,B and C. Tank A is filled while tank B and C are empty. If we poor oil in tank A into tank C, then $\frac{5}{9}$ of the oil remains in tank A. If we use the oil in tank A to fill in tank C and B, then 4 liters of oil will be needed. How many liters each tank can contain? 

A team joined a student contest in three subjects Literature, Math and English, held by the city council. They achieved 15 rewards. How many students are there in the team? Knowing that

Every students has a prize

At least 1 student gets 1 prize in every subject

At least 1 student gets 2 prizes in any two subjects

At least 1 student gets 3 prize in all three subjects.

The total number of students getting 3 awards, 2 awards and 1 ward increases in order.

Find the  four consecutive natural numbers from small to large so that the product of them is 3024 ?

Find the smallest natural number which has a remainder of 1 when it is divided by 2, has a remainder of 1 when it is divided by 5, has a remainder of 3 when it is divided by 7 and divisible by 9?