The length of each side of a rhombus is 10cm and one of its diagonal is of length 16cm. The Length of the other Diagonal is:a)5cmb)12cmc)13cmd)6cmCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Visualise a rhombus of each side 10 cm.

Now, we know that the diagonals of a rhombus are perpendicular bisectors i.e it is perpendicular to each other and divide each diagonal into two parts
since there are two diagonal so
there will be four parts out of which two parts of the same diagonal are equal .

So the diagonal of length 16cm is divided into two parts each of 8 cm

Since two diagonal are perpendicular bisectors of each other so it will divide the rhombus into four equal right angled triangle

visualising one triangle we get:

Hypotenuse =side of rhombus =10cm
one side whose measure os unknown =x (say)

another side =8 cm.
Applying phythogorus theorem

hypotenuse ² = base² (one side)+ perpendicular²

or,
hypotenuse²-base² =perpendicular ²
10² - 8²= perpendicular²
100-64 = perpendicular ²
36=perpendicular ²
6²=perpendicular ²
6=perpendicular

since diagonal is divided into two parts

total length of one diagonal =2×perpendular.
=2×6=12cm

Answer

Firstly we know that diagonal of rhombus bisects each other. thus half of diagonal =8cm.
by pythagoras theorem we find another half of diagonal.that is 6 cm
as we diagonals bisect other thus another diagonal
=2×6=12cm

Answer

Given:
Length of each side of the rhombus = 10 cm
Length of one diagonal = 16 cm

To find:
Length of the other diagonal

Explanation:
A rhombus is a quadrilateral with all four sides equal in length. It also has two diagonals that bisect each other at right angles.

Properties of a Rhombus:
- All sides are equal in length
- Opposite angles are equal
- Diagonals bisect each other at right angles

Step 1: Finding the Length of the Other Diagonal

Let's assume the length of the other diagonal is 'x' cm.

According to the properties of a rhombus, the diagonals bisect each other at right angles. Therefore, using the Pythagorean theorem, we can form the following equation:

(10/2)^2 + (x/2)^2 = 16^2
5^2 + (x/2)^2 = 16^2
25 + (x/2)^2 = 256
(x/2)^2 = 256 - 25
(x/2)^2 = 231

Taking the square root on both sides, we get:
x/2 = √231

Multiplying both sides by 2, we get:
x = 2√231

Step 2: Simplifying the Length of the Other Diagonal

To simplify the value of x, we need to find the prime factors of 231.

Prime factorization of 231:
231 = 3 * 7 * 11

Therefore, x = 2√(3 * 7 * 11)
x = 2√(231)
x = 2 * 11
x = 22

Conclusion:
The length of the other diagonal is 22 cm.

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