Answered

The lengths of the corresponding sides of 2 similar right triangles are in the ratio of 2:5. If the hypotenuse of the smaller triangle is 5 inches long, how many inches long is the hypotentuse of the larger triangle?

Answer :

Since the ratio is 2:5, it could be written as a fraction: 2/5. To make this apply to the sides of the triangles you'd have to create an equation where 2/5 equals 5/x, x being the length of the hypotenuse.

2/5 = 5/x

To get from 2 to 5, you'd have to multiply 2 by 2.5. Therefore, in order to make the equation equal, you have to multiply 5 (the denominator of 2/5) by 2.5.

2/5 = 5/12.5

The hypotenuse would be 12.5 inches long.

Using a rule of three, it is found that the hypotenuse of the larger triangle is 12.5 inches long.

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  • This question is solved by proportions, using a rule of three.
  • Ratio of 2:5 means that a length of 2 in the smaller triangle is worth a length of 5 in the large triangle.
  • When the length of the smaller triangle is 5, what is the length of the larger triangle?

2 inches - 5 inches

5 inches - x inches

Applying cross multiplication:

[tex]2x = 25[/tex]

[tex]x = \frac{25}{2}[/tex]

[tex]x = 12.5[/tex]

The hypotenuse of the larger triangle is 12.5 inches long.

A similar problem is given at https://brainly.com/question/23536327