Answer:
104
Step-by-step explanation:
A rhombus diagonal bisect each other so that means half of the diagonal is equal to the other half.
Applying that, this means
Since they are equal we can divide AC by 2 to find AE and EC.
20/2=10
AE=10, EC=10
Same for DB
48/2=24
DE=24, EB=24
A rhombus diagonals are perpendicular to each other so each middle angle will measure 90 degree.
Looking closer, a rhombus has 4 right triangles. We only need to use one.
Look at triangle AEB. We know AE=10 and EB=24 and Angle E=90. We can apply pythagorean theorem to find side AB.
[tex] {ae}^{2} + {db}^{2} = {ab}^{2} [/tex]
[tex] {10}^{2} + {24}^{2} = {ab}^{2} [/tex]
[tex]100 + 576 = ab {}^{2} [/tex]
[tex]676 = {ab}^{2} [/tex]
[tex] \sqrt{676} = 26[/tex]
The perimeter of rhombus is equal to
4a, where a is the length of one side.
One side measures 26 so we can plug that in.
[tex]26 \times 4 = 104[/tex]