The area of a parallelogram MNOP is 48 sq cm. MX, which is a line segment perpendicular to diagonal PN where X is on PN, is 3 cm. How to find the length of diagonal NP?
just use the area of the lower triangle with the 3 as the height... NP=16
To find the length of diagonal NP, you can use the formula for the area of a parallelogram.
The formula for the area of a parallelogram is given by:
Area = base x height
In this case, the base is the length of line segment MX, which is given as 3 cm. The height is the perpendicular distance between sides MN and OP.
Since line segment MX is perpendicular to diagonal PN, it can be considered as the height.
We are given that the area of parallelogram MNOP is 48 sq cm.
Therefore, we can use the formula and the given values to solve for the length of diagonal NP.
48 sq cm = 3 cm x height
To find the height, divide both sides of the equation by 3 cm:
height = 48 sq cm / 3 cm
height = 16 cm
Now, we can use the Pythagorean theorem to find the length of diagonal NP. In a parallelogram, the diagonals divide each other into equal halves.
Using the right triangle formed by diagonal PN, line segment MX (which is the height of the parallelogram), and half of the diagonal NP, we can apply the Pythagorean theorem:
(1/2 diagonal NP)^2 = height^2 + line segment MX^2
Let's substitute the values we know:
(1/2 diagonal NP)^2 = 16 cm^2 + 3 cm^2
Simplifying the equation further:
(1/2 diagonal NP)^2 = 256 cm^2 + 9 cm^2
(1/2 diagonal NP)^2 = 265 cm^2
To find the length of diagonal NP, we can take the square root of both sides:
1/2 diagonal NP = √265 cm
Now, let's solve for diagonal NP by multiplying both sides by 2:
diagonal NP = 2 * √265 cm
diagonal NP ≈ 32.53 cm
Therefore, the length of diagonal NP is approximately 32.53 cm.