Find the side $a$ of a rhombus if area $A = 30 cm$ and diagonal $d_{1} = 6.93 cm$ .

Answer

$5.545 cm$

Explanation

STEP 1: find diagonal $d 2$

To find diagonal $d 2$ use formula:

A = \frac{d _{1} \cdot d _{2}}{2}

After substituting $A = 30 cm$ and $d_{1} = 6.93 cm$ we have:

30 cm = \frac{6.93 cm \cdot d _{2}}{2}

30 cm \cdot 2 = 6.93 cm \cdot d_{2}

60 cm = 6.93 cm \cdot d_{2}

d_{2} = \frac{60 cm}{6.93 cm}

d_{2} = 8.658

STEP 2: find side $a$

To find side $a$ use formula:

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

After substituting $d_{1} = 6.93 cm$ and $d_{2} = 8.658 cm^{0}$ we have:

(6.93 cm)^{2} + 8.658 = 4 \cdot a^{2}

48.0249 cm^{2} + 74.9611 = 4 \cdot a^{2}

4 \cdot a^{2} = 122.986 cm^{2}

a^{2} = \frac{122.986 cm ^{2}}{4}

a^{2} = 30.7465 cm^{2}

a = 30.7465 cm^{2}

a = 5.545 cm

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Find the side a of a rhombus if area A=30cm and diagonal d1​=6.93cm.

5.545cm

Find the side $a$ of a rhombus if area $A = 30 cm$ and diagonal $d_{1} = 6.93 cm$ .

$5.545 cm$