Question

△DNS∼△ARH . What is the value of x? https://static.k12.com/nextgen_media/assets/8117851-NG_GMT_DP024_42_001.png

Answer 1

Given △DNS∼△ARH. (Refer to the attached image)

When triangles are similar, then the ratio all three pairs of corresponding sides are equal.

Since, △DNS∼△ARH

Therefore, $\frac{DN}{AR}=\frac{NS}{RH}=\frac{DS}{AH}$

Substituting the measurements of the corresponding sides.

$\frac{72}{21.6}=\frac{NS}{RH}=\frac{110}{x}$

Equating the first and last ratio of the corresponding sides,

$\frac{72}{21.6}=\frac{110}{x}$

Cross multiplying in the above equation, we get

$72 \times x = 110 \times 21.6$

$72 \times x = 2376$

$x=\frac{2376}{72}$

x= 33.

Therefore, the value of x is 33.

Answer 2

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