Question

0
In the figure, ABCD is a parallelogram in which AB = 20 cm,
BC=17 cm. If DE is perpendicular to AB and area of the parallelogram is
300 cm2, find AE.​

Answer 1

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Area of parallelogram = 300 cm²

AB = 20 cm

BC = AD = 17 cm

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Area of parallelogram = b × h

$300 \: {cm}^{2} = 20 \: cm \times h \\ h = \frac{300 \: {cm}^{2}}{20 \: cm} \\ h = 15 \: cm$

So, height of parallelogram = 15 cm

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In ∆ AED,

AD$\longrightarrow$20cm

ED$\longrightarrow$15cm

$AE = \sqrt{{AD}^{2} - {ED}^{2} } \\ AE = \sqrt{400 - 225} \\ AE = \sqrt{175} \\ AE = 5 \sqrt{7} cm$

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