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The diagonals of a rhombus are 16 cm and 12 cm, in length. The side of rhombus in length is:

(a) 20 cm

(b) 8 cm

(c) 10 cm

(d) 9 cm
​

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Answer:

(c) [tex]\displaystyle 10\:cm.[/tex]

Step-by-step explanation:

Split each diagonal in half and use the Pythagorean Theorem:

[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 8^2 + 6^2 = c^2 \hookrightarrow 64 + 36 = c^2 \hookrightarrow \sqrt{100} = \sqrt{c^2} \\ \\ \boxed{10 = c}[/tex]

I am joyous to assist you at any time.

Diagonals of a rhombus are perpendicular to each other .

  • Perpendicular=P=16/2=8
  • Base=B=12/2=6

We need Side

  • Hypotenuse=H

Use Pythagorean theorem

[tex]\\ \rm\rightarrowtail H^2=P^2+B^2[/tex]

[tex]\\ \rm\rightarrowtail H^2=6^2+8^2[/tex]

[tex]\\ \rm\rightarrowtail H^2=10^2[/tex]

[tex]\\ \rm\rightarrowtail H=10cm[/tex]

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