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△DNS∼△ARH .

What is the value of x?



Enter your answer in the box.

units

Triangle D N S with D N equal to 72 and D S equal to 110. Triangle A R H with A R equal to 21.6 and A H equal to x.

DNSARH What is the value of x Enter your answer in the box units Triangle D N S with D N equal to 72 and D S equal to 110 Triangle A R H with A R equal to 216 a class=

Respuesta :

ElenaClaudia
[tex]\Delta DNS \sim \Delta ARH \Longrightarrow \dfrac{DN}{AR} = \dfrac{DS}{AH} \\ \\ \dfrac{72}{21.6} = \dfrac{110}{x} \\ \\ \\ x = \dfrac{21.6 \times 110}{72} \\ \\ \\ x = \dfrac{2376}{72} \\ \\ \boxed{x = 33 \ units}[/tex]

The value of x in the given triangles similar by △DNS∼△ARH is;

x = 33

We are told that △DNS∼△ARH.

The symbol ∼ indicates that △DNS is similar to △ARH.

  • Now, according to formula to find ratio of similar sides of a triangle. we can apply it to our 2 triangles to get;

DN/AR = DS/AH = HR/SN

We can see that;

DN = 72

DS = 110

AR = 21.6

AH = x

Plugging in the relevant values into the similarity ratio formula, we have;

72/21.6 = 110/x

Making x the subject of the formula gives;

x = 110 × 21.6/72

x = 33

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