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The triangles are similar.


What is the value of x?


Enter your answer in the box.

x = ___
two right triangles. the larger triangle has a long leg of 72 units, a short leg labeled x, and a hypotenuse of 75 units. the smaller triangle has a long leg of 24 units, short leg of 7 units, and a hypotenuse of 25 units.

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lublana

Picture of the triangles is missing so let's draw two similar triangles ABC and DEF. Both are right angle triangle because hypotenuse occurs only in right angle triangle.

AB=72, AC=75, BC=x

DE=24, DF=25, EF=7

Now we can solve this problem in two ways.

Either use ratio for similar triangles or use Pythogorean theorem.

Taking ratio will be easy so let's do that.

Given that both triangles are similar so ratio of corresponding sides will be constant.

[tex] \frac{BC}{AB}=\frac{EF}{DE} [/tex]

[tex] \frac{x}{72}=\frac{7}{24} [/tex]

[tex] \frac{x}{72}*72=\frac{7}{24}*72 [/tex]

[tex] x=\frac{504}{24} [/tex]

x=21

Hence final answer is x=21.

Ver imagen lublana

The value of x = 21 units

According to the question , the 2 right angled triangle are similar.

Larger triangle

  • hypotenuse = 75 units
  • short leg = x
  • long leg = 72 unit

Smaller triangle

  • hypotenuse = 25 units
  • short leg = 7 units
  • long leg = 24 units

Using the following proportion, the value of x can be found below

75 / 25 = x / 7

cross multiply

25x = 525

x = 525 / 25

x = 21 units

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