How to find the perimeter of a rhombus

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ISEE Upper Level Quantitative Reasoning › How to find the perimeter of a rhombus

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One side of a rhombus measures 2 yards. Which of the following is equal to the perimeter?

$288 \textrm{ in }$

CORRECT

$18 \textrm{ ft}$

$12 \textrm{ yd}$

$\frac{1}{200} \textrm{ mi}$

All of the other choices give the correct perimeter.

A rhombus has four sides of equal measure, so the perimeter of a rhombus with sidelength 2 yards is $2 \times 4 = 8$ yards.

$8 \textrm{ yd} = 8 \times 3 = 24 \textrm{ ft} = 24 \times 12 = 288 \textrm{ in}$

Also,

$8 \textrm{ yd} = 24 \textrm{ ft} =\frac{ 24}{5,280} = \frac{1}{220} \textrm{ mi}$

The only choice that agrees with any of these measures is 288 inches, the correct choice.

One side of a rhombus measures . Give its perimeter in terms of .

CORRECT

$y^{2}+ 24y + 144$

$y^{2}+ 12y + 144$

A rhombus has four sides of equal measure, so the perimeter of a rhombus with sidelength is .