Question

9.The diagonals of a rhombus are 8 cm and 6 cm then the length of each side of the rhombus is equal to
(1 Point)
3 cm
4 cm
5 cm
None​

Answer 1

Answer:

option C (5 cm)

Step-by-step explanation:

Draw the rhombus ABCD, with AD and BC being drawn as horizontal lines, and AB and CD drawn starting at the lower left and moving to the upper right (so the shape is like a square that’s been pushed over to the right). (This way, we’re both looking at the same picture.) Let’s say that the length of AC is 8 and the length of BD is 6.

Draw the diagonals. Label the point where they cross as “F”.

Each of the four triangles formed by the two diagonals is congruent to the other three, so we need only work with one of them. Let’s use AFB.

This is a right triangle with right angle AFB, leg AF having length 4 and leg FB having length 3.

Use the Pythagorean Theorem to find the length of the hypotenuse, which is also the length of a side of the rhombus