ABCD a parallelogram in wich AB=6.5cm,AD=4.8cm,BD=5.7cm.what will be the measure of its diagonals
To find the measure of the diagonals of the parallelogram ABCD, we can use the properties of parallelograms.
In a parallelogram, opposite sides are equal in length and opposite angles are congruent.
Since AB = CD (opposite sides of the parallelogram) and AD = BC (opposite sides of the parallelogram), we can find the length of the diagonals by using the Pythagorean theorem.
Let's call the length of one diagonal as d1 and the length of the other diagonal as d2.
For diagonal d1, we can use triangle ABD where the diagonal acts as the hypotenuse. We have the lengths AB = 6.5 cm, BD = 5.7 cm, and we need to find d1.
Using the Pythagorean theorem, we have:
d1^2 = AB^2 + BD^2
d1^2 = 6.5^2 + 5.7^2
d1^2 = 42.25 + 32.49
d1^2 = 74.74
Taking the square root of both sides, we get:
d1 ≈ 8.65 cm
For diagonal d2, we can use triangle ACD where the diagonal acts as the hypotenuse. We have the lengths AD = 4.8 cm, CD = AB (since opposite sides of a parallelogram are equal), and we need to find d2.
Using the Pythagorean theorem, we have:
d2^2 = AD^2 + CD^2
d2^2 = 4.8^2 + 6.5^2
d2^2 = 23.04 + 42.25
d2^2 = 65.29
Taking the square root of both sides, we get:
d2 ≈ 8.09 cm
Therefore, the measure of one diagonal (d1) is approximately 8.65 cm and the measure of the other diagonal (d2) is approximately 8.09 cm.