Question

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Answer 1

Answer:

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

Step-by-step explanation:

Split each diagonal in half and use the Pythagorean Theorem:

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

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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

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

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

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

$\\ \rm\rightarrowtail H=10cm$