Question

find the perimeter of a rhombus if the diagonal are 6cm and 8 cm

Answer 1

Answer on Question #45217 – Math – Geometry

find the perimeter of a rhombus if the diagonal are 6cm and 8 cm

Solution:

Diagonal 6cm = 3cm + 3cm = legs of right triangle within rhombus.

Diagonal 8cm = 4cm + 4cm = legs of right triangle within rhombus.

We need to find the side of the rhombus using the Pythagorean Theorem, because diagonals of rhombus are perpendicular.

Let $s =$ side of rhombus.

P = perimeter of the rhombus

After that, we use the formula $P = 4 \cdot s$ to find perimeter.

Pythagorean Theorem for the right triangle:

$$3^2 + 4^2 = s^2$$ $$\begin{array}{l} 9 + 16 = s^2 \\ 25 = s^2 \\ s = 5 \\ \end{array}$$

Now that we know the side of the rhombus, apply $P = 4 \cdot s$.

$$P = 4 \cdot 5 \text{cm} = 20 \text{cm}$$

Answer: perimeter of a rhombus is 20cm

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