RSTV is a Rhombus. RT = 16cm and SV = 12cm. Find the perimeter of the rhombus below
To solve the problem you mus apply the folllowing proccedure:
1. You have that the rhombus RSTV is RT = 16 cm and SV = 12cm. Therefore, to calculate the area you must apply the formula for calculate the area of a rhombus, as below:
A=(RT)(SV)/2
2. Therefore, when you susbtitute the values of RT and SV into the formula shown above, you obtain the the area of the rhombus is:
A=(16 cm)(12 cm)/2
A=96 cm²
3. Then, as you can see, the answer is:
The area of the rhombus is 96 cm².
Permiter**
The diagonals are perpendicular, and bisect each other. So they divide the rhombus into four congruent right triangles, each with hypotenuse = 10.
So the perimeter is 4*10 = 40
To find the perimeter of the rhombus, we need to know the length of all four sides. However, we only have information about two sides, RT and SV.
A rhombus is a quadrilateral with all sides of equal length. In this case, we can assume that RS and TV are also equal in length to RT and SV.
To find the length of RS and TV, we can apply the properties of a rhombus.
In a rhombus, opposite sides are parallel and opposite angles are congruent. The diagonals of a rhombus bisect each other at right angles.
Let's use the information we have to find the length of RS and TV.
We know that RT = 16 cm and SV = 12 cm.
Since RS and TV are opposite sides, they must also be equal in length. Therefore, RS = 16 cm.
Now, let's find the length of TV.
The diagonals of a rhombus bisect each other at right angles. This means that the line segment connecting the midpoints of RT and SV is perpendicular to both RT and SV.
Let's call the intersection point of RS and TV as point X. Since X is the midpoint of RT, RX = 16/2 = 8 cm.
Similarly, since X is the midpoint of SV, SX = 12/2 = 6 cm.
Now we can use the Pythagorean theorem to find the length of TV.
In triangle RSX, RX = 8 cm and SX = 6 cm.
Using the Pythagorean theorem, we can find the length of TV.
RS^2 = RX^2 + SX^2
16^2 = 8^2 + 6^2
256 = 64 + 36
256 = 100
Taking the square root of both sides:
RS = √100
RS = 10 cm
Since RS = TV, TV is also 10 cm.
Now we have the lengths of all four sides of the rhombus: RT = 16 cm, RS = 10 cm, SV = 12 cm, and TV = 10 cm.
To find the perimeter of the rhombus, we add up all four sides:
Perimeter = RT + RS + SV + TV
Perimeter = 16 + 10 + 12 + 10
Perimeter = 48 cm
Therefore, the perimeter of the rhombus is 48 cm.