Question #158222

The diagonals of a rhombus are 10 centimeters

and 24 centimeters. Find the

perimeter of the rhombus.



1
Expert's answer
2021-02-02T05:15:33-0500

In any rhombus, the diagonals  bisect each other at right angles (90°). 

Assume aa is the side of the rhombus, d1d_1 and d2d_2 are its diagonals

d1=10 cm,d2=24 cm.d_1=10\ cm, d_2=24\ cm.

By the Pythagorean Theorem


a2=(d12)2+(d22)2a^2=(\dfrac{d_1}{2})^2+(\dfrac{d_2}{2})^2

a=(102)2+(242)2=13(cm)a=\sqrt{(\dfrac{10}{2})^2+(\dfrac{24}{2})^2}=13(cm)

Find the perimeter of the perimeter


P=4a=4(13 cm)=52 cmP=4a=4(13 \ cm)=52\ cm

The perimeter of the rhombus is 52 centimeters.



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