Answered

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The length of the shorter diagonal of a rhombus is 10 centimeters. Determine the length of the longer diagonal, to the nearest centimeter, if the perimeter

of the rhombus is 52 centimeters.

Length of the longer diagonal

cm

Sagot :

abidemiokin

Answer:

24cm

Step-by-step explanation:

Perimeter of a rhombus = 4a

a is the side of the rhombus

52 = 4a

a = 52/4

a = 13cm

If the length of the shorter diagonal of a rhombus is 10 centimeters, then the  length of the other diagonal is expressed as;

L = 2 * √a²-(s/2)²

s is the length of the shorter diagonal

Given

a = 13cm and s = 10cm, substitute

L = 2 * √13²-(10/2)²

L = 2*√169-5²

L = 2*√169-25

L = 2*√144

L = 2*12

L = 24cm

Hence the length of the longer diagonal is 24cm

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