Question

The perimeter of a rhombus is $52cm$ and one of its diagonals is $10cm$. Find the length of the other diagonal and area of a rhombus.

Answer 1

We have,

Parameter of a rhombus$=52cm.$

Its diagonal$=10cm.$

Let the length of the other diagonal$=xcm$

Area of rhombus $=?$

Now,

Parameter of rhombus $=4\times side$

$52=4\times side$

$\Rightarrow side=13cm.$

Therefore, each side of rhombus $=13cm.$

Then, the length of other diagonal$=2\sqrt{{13}^2-{\left(\frac{10}{2}\right)}^2}$

$x=2\sqrt{169-25}$

$x=2\times \sqrt{144}$

$x=2\times 12$

$x=24cm.$

We know that,

Area of rhombus$=\frac{1}{2}\times$ product of diagonals

$=\frac{1}{2}\times 10\times 24$

$=5\times 24$

$=120cm{.}^2$

Hence, this is the answer