Diagonals of a rhombus 2

One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm², find the side of the rhombus.

Correct result:

a =  10 cm

Solution:

$$\begin{gathered} u=4+v=4+12=16 \\ S=96{\text{cm}}^2 \\ S={\displaystyle \frac{uv}{2}}={\displaystyle \frac{(4+v)v}{2}} \\ 96=(4+v)\ast v\mathrm{/}2 \\ 96=(4+v)\cdot v\mathrm{/}2 \\ -0.5v^2-2v+96=0 \\ 0.5v^2+2v-96=0 \\ a=0.5;b=2;c=-96 \\ D=b^2-4ac=2^2-4\cdot 0.5\cdot (-96)=196 \\ D>0 \\ {v}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{-2\pm \sqrt{196}}{1}}=-2\pm 14\sqrt{1} \\ {v}_{1,2}=-2\pm 14 \\ {v}_1=12 \\ {v}_2=-16 \\ \text{ Factored form of the equation: } \\ 0.5(v-12)(v+16)=0 \\ v=v_1=12=12\text{ cm } \\ u=4+v=4+12=16\text{ cm } \\ a=\sqrt{(u\mathrm{/}2{)}^2+(v\mathrm{/}2{)}^2}=\sqrt{(16\mathrm{/}2{)}^2+(12\mathrm{/}2{)}^2}=10\text{ cm} \end{gathered}$$

Our quadratic equation calculator calculates it.

Try another example

Showing 0 comments:

Related math problems and questions:

• Diamond diagonals
  Find the diamond diagonal's lengths if the area is 156 cm² and side is 13 cm long.
• Diamond diagonals
  Calculate the diamond's diagonal lengths if its content is 156 cm² and the side length is 13 cm.
• Diamond diagonals
  Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square, and the side length is 13 cm.
• Diagonals of the rhombus
  How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm²?
• Two diagonals
  The rhombus has a side length 12 cm and length of one diagonal 21 cm. What is the length of the second diagonal?
• Diagonals
  A diagonal of a rhombus is 20 cm long. If it's one side is 26 cm find the length of the other diagonal.
• Rhombus and diagonals
  The a rhombus area is 150 cm² and the ratio of the diagonals is 3:4. Calculate the length of its height.
• Diagonals in diamons/rhombus
  Rhombus ABCD has side length AB = 4 cm and a length of one diagonal of 6.4 cm. Calculate the length of the other diagonal.
• Rhombus
  The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
• Diagonals of a rhombus
  One of the diagonals of a rhombus is twice as the other. If the sum of the lengths of the diagonals is 24, find the area of the rhombus.
• Rectangle diagonals
  It is given rectangle with area 24 cm² a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
• Rhombus
  The rhombus with area 68 has one diagonal is longer by 6 than second one. Calculate the length of the diagonals and rhombus sides.
• Rhombus and inscribed circle
  It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
• Two diagonals
  The diagonals of the diamond EFGH have lengths in the ratio 1: 2. What is the circumference of a rhombus if the longer of the diagonals is 8 cm long?
• Rhombus
  One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.
• Diagonals
  Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus.
• Rectangle
  There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.