Question

The adjacent sides of a parallelogram are in the ratio 4 : 5. Find their
lengths if the perimeter is 90 cm.

Answer 1

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Answer 2

$\bold{ \underline{Question :} }$

The adjacent sides of a parallelogram are in the ratio 4 : 5. Find their lengths if the perimeter is 90 cm.

$\bold{ \underline{Answer:} }$

$\bold{ \leadsto \: Side \: with \: length \: 4x = 20 \: cm} \: \: \: \\ \bold{\leadsto \:Side \: with \: length \: 5x = 25\: cm} \: \: \:$

$\bold{ \underline{Explanation:} }$

$\sf \: Let \: adjacent \: sides \: as \: 4x \: and \: 5x .$

$\sf Perimeter \: of \: parallelogram = 90 \:cm$

$\sf Perimeter \: of \: parallelogram = 2(a + b) \\ \begin{cases} \sf \: where \: a = 4x \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: b = 5x \end{cases} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\sf Perimeter \: of \: parallelogram = 2(4x + 5x) \\ \leadsto \sf90 = 2 \times 9x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\leadsto \sf90 =18x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \leadsto\sf18x = 90 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \leadsto\sf x = \frac{ \cancel{90}}{\cancel{18}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \purple{ \boxed{\sf x = 5 \: cm}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\bold{ \leadsto \: Side \: with \: length \: 4x = 20 \: cm} \: \: \: \\ \bold{\leadsto \:Side \: with \: length \: 5x = 25\: cm} \: \: \:$