Find the perimeter $P$ of a rhombus if diagonal $d_{1} = 16 cm$ and diagonal $d_{2} = 12 cm$ .

Answer

$40 cm$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

d_{1}^{2} + d_{2}^{2} = 4 \cdot a^{2}

After substituting $d_{1} = 16 cm$ and $d_{2} = 12 cm$ we have:

(16 cm)^{2} + (12 cm)^{2} = 4 \cdot a^{2}

256 cm^{2} + 144 cm^{2} = 4 \cdot a^{2}

4 \cdot a^{2} = 400 cm^{2}

a^{2} = \frac{400 cm ^{2}}{4}

a^{2} = 100 cm^{2}

a = 100 cm^{2}

a = 10 cm

STEP 2: find perimeter $P$

To find perimeter $P$ use formula:

P = 4 \cdot a

After substituting $a = 10 cm$ we have:

P = 4 \cdot 10 cm

P = 40 cm

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Find the perimeter P of a rhombus if diagonal d1​=16cm and diagonal d2​=12cm.

40cm

Find the perimeter $P$ of a rhombus if diagonal $d_{1} = 16 cm$ and diagonal $d_{2} = 12 cm$ .

$40 cm$