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In the rhombus shown above, AC = 20 and DB = 48. Find the perimeter of the rhombus.

In The Rhombus Shown Above AC 20 And DB 48 Find The Perimeter Of The Rhombus class=

Sagot :

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

  • AE=EC
  • DE=EB

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]