Question

The side of a rhombus is 13cm. if the length of one diagonal is 24cm , then find the length​

Answer 1

the diagonals of a rhombus intersect in the middle and are perpendicular to each other i suppose we're looking for the length of the other diagonal

rhombus ABCD center O

diagonal AC, AO = 24/2 = 12

AC diagonal: AOB rectangle in O

we know AB=13cm, BO =12cm we're looking for OB (half-diagonal BD)

AOB rectangle

AB²=AO²+OB²

13²=12²+OB²

OB²=13²12²

OB = √25 = 5cm

other diagonal length =10cm

Answer 2

The length of the second diagonal of the rhombus is 10cm, determined by using the properties of a 5-12-13 right triangle created by bisecting the given 24cm diagonal.

Step-by-step explanation:

To find the length of the second diagonal of a rhombus, we can use the properties of right triangles. Given one diagonal is 24cm, it can be bisected into two equal segments of 12cm each. Alongside this, the rhombus's side of 13cm becomes the hypotenuse of these right triangles. From the properties of a 5-12-13 right triangle, we can infer the two halves of the second diagonal are each 5cm, thus the whole diagonal is 10cm.

Here's how we determine this step by step:

1. The first diagonal of the rhombus is 24cm in length, which when bisected by the perpendicular second diagonal, creates two right triangles, each with a side of 12cm.
2. The side of the rhombus, which is 13cm, acts as the hypotenuse for these right triangles.
3. Using the Pythagorean triplet (5-12-13), we can determine the other side of these right triangles must be 5cm, as the hypotenuse is 13cm and one side is 12cm.
4. Since there are two triangles formed by this second diagonal, the full length of the second diagonal is 5cm times 2, which is 10cm.