# Examples for 9th grade - page 37

- Similarity

Rectangle ABCD has dimensions of 7 cm and 6 cm. Rectangle PQRS has dimensions 14 cm and 12 cm. Determine coefficient of the similarity k of the rectangles, if they aren't similar enter zero as the coefficient of similarity. - Flowerbed

Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex? - Diagonal in rectangle

In that rectangle ABCD is the center of BC point E and point F is center of CD. Prove that the lines AE and AF divide diagonal BD into three equal parts. - Trousers

Jarek bought new trousers, but the trousers were too long. Their length was in the ratio 5: 8 to Jarek height. Mother his trousers cut by 4 cm, thus the original ratio decreased by 4%. Determine Jarek's high. - Scouts

Three scouts went on a three day trip. The second day went 4 km more than the first day. The third day went two times less than the first day. They went along 54 km. How many kilometers went every day together? - Sphere area

A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere. - Simple interest 4

Find the simple interest if 5243 USD at 4.3% for 261 days. Assume a 361-day year. - Acreage

What acreage has a rectangular plot whose diagonal is 34 meters long and one side has a length of 16 meters. ? - BW-BS balls

Adam has a full box of balls that are large or small, black or white. Ratio of large and small balls is 5:3. Within the large balls the ratio of the black to white is 1:2 and between small balls the ratio of the black to white is 1:8 What is the ratio of. - Bevel

I have bevel in the ratio 1:6. What is the angle and how do I calculate it? - Secret number

Determine the secret number n, which reversed decrease by 16.4 if the number increase by 16.4. - Slope

What is the slope of the line defined by the equation -2x +3y = -1 ? - Pool 2

The first supply by the pool fill for five hours and the second fill for six hours, drain should be drained for 15 hours. For how many hours the pool is full, when we open both inlet now and outlet open two hours later? - Rope

How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)? - Word problem

395 students were on holiday in Hungary. 110 bought pizza, chips 21 pupils, 26 pupils bought soda, butter 18 pupils, 12 pupils fruits, vegetables 29 students. How much pay for all the food, if every meal cost 5.5 euros? - Digits A, B, C

For the various digits A, B, C is true: the square root of the BC is equal to the A and sum B+C is equal to A. Calculate A + 2B + 3C. (BC is a two-digit number, not a product). - Three numbers

The sum of the three numbers is 287. These numbers are in a ratio of 3: 7: 1/4 Define these numbers - Cylinder

The cylinder surface is 859 dm^{2,}its height is equal to the radius of the base. Calculate height of this cylinder. - Vinegar

What percentage vinegar we get if we mix 1 if dm³ eight percent vinegar with 1.5 dm³ six percent vinegar? - Medal

Calculate the approximate weight of the gold Olympics medal, if its diameter is 8 cm and a thickness 6 mm. The density of gold find out in the tables or on the Internet.

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