In rhombus ABCD,AC = 24 and BD = 70. Find the | vedclass

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(A) rhombus is a quadrilateral where all sides are equal and diagonals bisect each other at right angles $(90^{\circ})$.Let the diagonals be $d_1 = AC

Vedclass · Accepted Answer

$148$

Vedclass · Answer

(A) rhombus is a quadrilateral where all sides are equal and diagonals bisect each other at right angles $(90^{\circ})$.Let the diagonals be $d_1 = AC = 24$ and $d_2 = BD = 70$.The diagonals bisect each other at point $O$. Thus,the segments are $AO = OC = \frac{24}{2} = 12$ and $BO = OD = \frac{70}{2} = 35$.In the right-angled triangle $	riangle AOB$,by the Pythagorean theorem:$AB^2 = AO^2 + BO^2$$AB^2 = 12^2 + 35^2$$AB^2 = 144 + 1225 = 1369$$AB = \sqrt{1369} = 37$.The perimeter of the rhombus is $4 	imes 	ext{side} = 4 	imes 37 = 148$.

In rhombus $ABCD$,$AC = 24$ and $BD = 70$. Find the perimeter of rhombus $ABCD$.

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