Question

Hello people ~

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
​

Answer 1

(c)
`\displaystyle 10\:cm.`

Step-by-step Step-by-step explanation:

Split each diagonal in half and use the Pythagorean Theorem:

`\displaystyle a^2 + b^2 = c^2 \\ \\ 8^2 + 6^2 = c^2 \hookrightarrow 64 + 36 = c^2 \hookrightarrow √(100) = √(c^2) \\ \\ \boxed{10 = c}`

I am joyous to assist you at any time.

Answer 2

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

`\\ \rm\rightarrowtail H^2=P^2+B^2`

`\\ \rm\rightarrowtail H^2=6^2+8^2`

`\\ \rm\rightarrowtail H^2=10^2`

`\\ \rm\rightarrowtail H=10cm`