Question 1089943


A rhombus is a flat shape with {{{4}}} equal straight sides.
Opposite sides are parallel, and opposite angles are equal (it is a parallelogram).
And the diagonals "{{{p}}}" and "{{{q}}}" of a rhombus bisect each other at {{{right}}} angles.

Perimeter: {{{P = 4s}}}

if the perimeter of a rhombus is {{{40cm}}} and one of its diagonals is {{{12cm}}}, we have:

{{{4s=40cm}}}
{{{s=40cm/4}}}
{{{s=10cm}}}

so, we have:
side {{{s=10cm}}}
diagonal {{{p=12cm}}}

since {{{s}}}, {{{p/2}}}, and {{{q/2}}} form right triangle, we can find {{{q/2}}} using Pythagorean theorem:

{{{s^2=(q/2)^2+(p/2)^2}}}

{{{(10cm)^2-(12cm/2)^2=(q/2)^2}}}

{{{(q/2)^2=100cm^2-(6cm)^2}}}

{{{(q/2)^2=100cm^2-36cm^2}}}

{{{(q/2)^2=64cm^2}}}

{{{q/2=sqrt(64cm^2)}}}

{{{q/2=8cm}}}

{{{q=8cm*2}}}

{{{q=16cm}}}

so, the length of the other diagonal is {{{16cm}}}