how to find the diagonal of a rhombus if the lengths are given
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how to find the diagonal of a rhombus if the lengths are given
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Answer:
To find the value of diagonal FH¯¯¯¯¯¯¯¯¯, we must first recognize some important properties of rhombuses. Since the perimeter is of EFGH is 24, and by definition a rhombus has four sides of equal length, each side length of the rhombus is equal to 6. The diagonals of rhombuses also form four right triangles, with hypotenuses equal to the side length of the rhombus and legs equal to one-half the lengths of the diagonals. We can therefore use the Pythagorean Theorem to solve for one-half of the unknown diagonal:
62=52+x2, where 6 is the rhombus side length, 5 is one-half of the known diagonal, and x is one-half of the unknown diagonal. We can therefore solve for x:
x2=62−52=36−25=11
x is therefore equal to 11−−√. Since x represents one-half of the unknown diagonal, we need to multiply by 2 to find the full length of diagonal FH¯¯¯¯¯¯¯¯¯.
The length of diagonal FH¯¯¯¯¯¯¯¯¯ is therefore 211−−√