# The sides 2

The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.

Result

h =  14
o =  70

#### Solution:

$a:b:c:d=2:5:8:5 \ \\ a=8x \ \\ b=d=5x \ \\ c=2x \ \\ a || c \ \\ \ \\ S=245 \ \\ \ \\ h=\sqrt{ d^2 - ((a-c)/2)^2 } \ \\ h=x \cdot \ \sqrt{ 5^2 - ((8-2)/2)^2 } \ \\ \ \\ h=x \cdot \ \sqrt{ 5^2 - ((8-2)/2)^2 } \ \\ h=x \cdot \ \sqrt{ 16 } \ \\ h=4x \ \\ \ \\ S=\dfrac{ a+c }{ 2 } h \ \\ S=\dfrac{ 8x+2x }{ 2 } h \ \\ S=\dfrac{ 8x+2x }{ 2 } \cdot \ 4x \ \\ S=5x \cdot \ 4x \ \\ x=\sqrt{ S/20 }=\sqrt{ 245/20 }=\dfrac{ 7 }{ 2 }=3.5 \ \\ \ \\ h=4 \cdot \ x=4 \cdot \ 3.5=14$
$a=8 \cdot \ x=8 \cdot \ 3.5=28 \ \\ b=5 \cdot \ x=5 \cdot \ 3.5=\dfrac{ 35 }{ 2 }=17.5 \ \\ d=5 \cdot \ x=5 \cdot \ 3.5=\dfrac{ 35 }{ 2 }=17.5 \ \\ c=2 \cdot \ x=2 \cdot \ 3.5=7 \ \\ \ \\ S_{1}=\dfrac{ a+c }{ 2 } \cdot \ h=\dfrac{ 28+7 }{ 2 } \cdot \ 14=245 \ \\ S_{1}=S \ \\ \ \\ o=a+b+c+d=28+17.5+7+17.5=70$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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

Showing 1 comment:
Math student
I don't understand.

Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.

## 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. Land - isosceles trapezoid
Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
3. Roof tiles
The roof has a trapezoidal shape with bases of 15 m and 10 m, height of roof is 4 meters. How many tiles will need if on 1 m2 should be used 8 tiles?
4. Length IT
Find the length (circumference) of an isosceles trapezoid in which the length of the bases a,c and the height h are given: a = 8 cm c = 2 cm h = 4 cm
5. 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?
6. The ditch
Ditch with cross section of an isosceles trapezoid with bases 2m 6m are deep 1.5m. How long is the slope of the ditch?
7. Estate
Estate shaped rectangular trapezoid has bases long 34 m , 63 m and perpendicular arm 37 m. Calculate how long is its fence.
8. Isosceles triangle
Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm.
9. 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?
10. Equilateral triangle
The equilateral triangle has a 23 cm long side. Calculate its content area.