# Diamond diagonals

Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.

Correct result:

u =  21.633 cm
v =  14.422 cm

#### Solution:

$S=156 \ \text{cm}^2 \ \\ a=13 \ \text{cm} \ \\ S=uv/2 \ \\ a^2=(u/2)^2+(v/2)^2 \ \\ 4a^2=u^2 + v^2 \ \\ 676=u^2+v^2 \ \\ 312=uv \ \\ v=312/u \ \\ 676=u^2+(312/u)^2 \ \\ x=u^2 \ \\ 676=x+312^2/x \ \\ \ \\ 676x=x^2+312^2 \ \\ \ \\ -x^2 +676x -97344=0 \ \\ x^2 -676x +97344=0 \ \\ \ \\ a=1; b=-676; c=97344 \ \\ D=b^2 - 4ac=676^2 - 4\cdot 1 \cdot 97344=67600 \ \\ D>0 \ \\ \ \\ x_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ 676 \pm \sqrt{ 67600 } }{ 2 } \ \\ x_{1,2}=\dfrac{ 676 \pm 260 }{ 2 } \ \\ x_{1,2}=338 \pm 130 \ \\ x_{1}=468 \ \\ x_{2}=208 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -468) (x -208)=0 \ \\ \ \\ u=\sqrt{ x_{1} }=\sqrt{ 468 }=6 \ \sqrt{ 13 }=21.633 \ \text{cm}$

Checkout calculation with our calculator of quadratic equations.

$v=\sqrt{ x_{2} }=\sqrt{ 208 }=4 \ \sqrt{ 13 }=14.422 \ \text{cm}$ 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!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors. Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a system of equations and looking for calculator system of linear equations?
Do you want to convert length units?
Pythagorean theorem is the base for the right triangle calculator.

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Block or cuboid The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
• Nice prism Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.
• Solid cuboid A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has length 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
• Diagonal 20 Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be?
• Three faces of a cuboid The diagonal of three faces of a cuboid are 13,√281 and 20 units. Then the total surface area of the cuboid is.
• Faces diagonals If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.3, y=1, z=1.2
• Three parallels The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.
• Two chords Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
• Isosceles trapezoid Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
• AP RT triangle The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
• Sides of right angled triangle One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.
• Right triangle eq2 Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
• An equilateral An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
• Find the 13 Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4].
• Touch x-axis Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
• Sphere from tree points Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
• A bridge A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water.