The area of the rhombus is 540 cm2; the length of one of its diagonals is 4.5 dm. what is the distance between the point of intersection of the diagonals and the side of the rhombus?

Given: Area of rhombus is 540 square cm and the length of one of its diagonals is 4.5 dm

To find the other diagonal of the rhombus:

Using formula of Area of rhombus:

Area of rhombus(A) =  ......[1]; where are the diagonals and A is the area of rhombus respectively.

Use conversion:

1 dm = 10 cm

then;

4.5 dm = cm

Substitute the value of A = 540 square cm and in [1] we have;

or

Divide by 45 both sides we get;

The distance between the point of intersection of the diagonals and the side of the rhombus :

The line perpendicular to the rhombus side i,e x the altitude to the hypotenuse of one of those right triangles.

The length x of such an altitude in a right triangle with leg lengths  and can be found from:

then:

or

or

Simplify:

x ≈ 10.59

Therefore, the distance between the point of intersection of the diagonals and the side of the rhombus is, 10.59 cm

this was already solved by me with a different person. if you look it up in the search bar at the top of the page, you will get the answer.

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is