Question

If the diagonals of a rhombus measure $10$cm and $24$cm, find its perimeter.

Answer 1

R.E.F.image

Given that,

Diagonals of the rhombus $10,24$ cm

since the diagonals meet at the center of the rhombus,

they create $4$ right angles in the center.

so in this, we can use the Pythagoras theorem, which

states that the sum of squares on the height and

the base of a right angle is equal is square on the

hypotenuse.

Length of the base $=\frac{10}{2}=5$ cm

Length of the height = $\frac{24}{2}=12$ cm.

By Pythagoras theorem,

Hypotenuse$=(5{)}^2+(12{)}^2$

$(AB{)}^2=25+144$

$(AB{)}^2={169}^2=AB=\sqrt{(13{)}^2}$

$\therefore$ Hypotenuse $=13$ cm

So, the side of a rhombus is $13$ cm.

the perimeter of the rhombus =$4\times side$

=$4\times 13$

=$52$ cm

Therefore, the perimeter of the rhombus is $52$ cm.