Mathematics, 26.07.2019 00:00 ChocCole

The area of the rhombus is 480 cm2; the length of one of its diagonals is 4.8 dm. what is the distance between the point of intersection of the diagonals and the side of the rhombus?

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Recall that a rhombus is a particular kind of parallelogram: the length you are looking for will be half of the parallelogram's height.

First, find the second diagonal of the rhombus:
d₂ = 2·A / d₁
= 2·480 / 48 *we transformed the units of measurement from dm to cm
= 20 cm

Now, consider the small triangle rectangle formed by the side of the rhombus and the halves diagonals. You can apply the Pythagorean theorem in order to find the side:
s = √[(d₁ /2)² + (d₂ / 2)²]
   =√[(48 / 2)² + (20 / 2)²]
   = 26 cm

Now, the side of the rhombus is the base of the parallelogram, therefore:
h = A / s
   = 480 / 26
   = 18.46 cm

The distance between the point of intersection of the diagonals and the side of the rhombus will be:
18.46 ÷ 2 = 9.23 cm

Answer from: ahoney2233

Area of the rhombus is half of the product of the both the diagonal. The distance between side and point of intersection of the diagonals is 9.23 cm.

Given information-

The area of the rhombus is 480 squared cm.

The length of one of its diagonals is 4.8 dm.

As the 1 dm is equal to the 10 cm. Thus,

The length of one of its diagonals is 48 cm.

Area of rhombus

Area of the rhombus is half of the product of the both the diagonal. Suppose the length of the another diagonal of the rhombus is x cm. thus,

$480=\dfrac{4.8\times x}{2} \\
x=\dfrac{2\times480}{48} \\
x=20$

Thus the length of the another diagonal is 20 cm.

The side of the rhombus can be given as,

$s=\sqrt{(\dfrac{48}{2})^2 +(\dfrac{20}{2})^2 }$

s=26

Thus the side of the rhombus is 26 cm.

As the area of the rhombus is the product of its height and side. Let is the height of the rhombus. Thus,

$480=h\times26$

Solve for ,

$h=\dfrac{480}{26} \\
h=18.46$

The distance between side and point of intersection of the diagonals of rhombus is half of the height. thus,

$d=\dfrac{18.46}{2} \\
d=9.23$

Thus the distance between side and point of intersection of the diagonals is 9.23 cm.

Learn more about the area of the rhombus here;

link

Answer from: Quest

right

step-by-step explanation:

Answer from: Quest

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

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The area of the rhombus is 480 cm2; the length of one of its diagonals is 4.8 dm. what is the dista...

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