Squares above sides

Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm². The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calculate the length of the AB side in cm.
Calculate the area of the square above the AC side in cm².

Result

c =  12 cm
S₂ =  73 cm²

Solution:

$S_{1}=25 \ \text{cm}^2 \ \\ a=\sqrt{ S_{1} }=\sqrt{ 25 }=5 \ \text{cm} \ \\ v=3 \ \text{cm} \ \\ \ \\ c_{1}^2=a^2 - v^2 \ \\ c_{1}=\sqrt{ a^2-v^2 }=\sqrt{ 5^2-3^2 }=4 \ \text{cm} \ \\ \ \\ c_{2}:c_{1}=2:1=2 \ \\ \ \\ c_{2}=c_{1} \cdot \ 2=4 \cdot \ 2=8 \ \text{cm} \ \\ \ \\ c=c_{1}+c_{2}=4+8=12 \ \text{cm}$

$b^2=c_{2}^2 + v^2 \ \\ \ \\ b=\sqrt{ c_{2}^2 + v^2 }=\sqrt{ 8^2 + 3^2 } \doteq \sqrt{ 73 } \ \text{cm} \doteq 8.544 \ \text{cm} \ \\ \ \\ S_{2}=b^2=8.544^2=73 \ \text{cm}^2$

Try calculation via our triangle calculator.

Try another example

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. Sum of squares
   The sum of squares above the sides of the rectangular triangle is 900 cm². Calculate content of square over the triangle's hypotenuse.
2. Silver medal
   To circular silver medal with a diameter of 10 cm is inscribed gold cross, which consists of five equal squares. What is the content area of silver part?
3. Free space in the garden
   The grandfather's free space in the garden was in the shape of a rectangular triangle with 5 meters and 12 meters in length. He decided to divide it into two parts and the height of the hypotenuse. For the smaller part creates a rock garden, for the large
4. Square
   Calculate the area of the square shape of the isosceles triangle with the arms 50m and the base 60m. How many tiles are used to pave the square if the area of one tile is 25 dm²?
5. Land
   Rectangular triangular land has area 30 square meters and 12 meters long leg. How many meters of the fence do you need for fencing this land?
6. Equilateral triangle
   The equilateral triangle has a 23 cm long side. Calculate its content area.
7. Isosceles trapezoid
   Calculate the area of an isosceles trapezoid whose bases are in the ratio of 4:3; leg b = 13 cm and height = 12 cm.
8. Isosceles triangle
   Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm.
9. Isosceles trapezium
   Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm.
10. Median in right triangle
    In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
11. Median
    In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.
12. Double ladder
    The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
13. Isosceles trapezoid
    What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm?
14. Double ladder
    The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
15. A truck
    A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
16. Center traverse
    It is true that the middle traverse bisects the triangle?
17. Holidays - on pool
    Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?