Question

. ABCD is a rhombus in which AC = 16 cm ;
BC = 10 cm. Find the length of the diagonal BD

Answer 1

see the image for the answer

Answer 2

The length of the diagonal BD is 18.6 cm.

• A rhombus is a special type of parallelogram in which all four sides have the same length. In this problem, we are given two sides of the rhombus, AC and BC, and we need to find the length of the diagonal BD.

• We know that the diagonals of a rhombus are perpendicular to each other and they bisect each other at 90 degree. Also, the diagonals of a rhombus divide it into four congruent right triangles.

• So, we can use the Pythagorean Theorem to find the length of BD. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Therefore,

BD = √(AC² + BC²) = √(16² + 10²) = √(256 + 100) = √356 = 18.6

So, The length of the diagonal BD is 18.6 cm.

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