Question

HELP FAST PLEASE

Juan drew a right triangle with leg length of 6 centimeters and 8 centimeters he wants to draw another triangle that is similar to the first one what could be the length of the legs

A. 9 centimeters and 16 centimeters

B. 18 cm and 24 centimeters

C. 16 centimeters and 18 centimeters

D. 3 centimeters and 5 centimeters

Answer 1

B 18 and 24

6x3=18

8x3=24

Answer 2

Option: B is the correct answer.

B. 18 cm and 24 centimeters

Explanation:

We know that if two triangles are similar than the ratio of the corresponding sides of the two triangles are equal.

i.e. if there is a triangle with side lengths a,b and c units respectively and other triangle with the corresponding side lengths a',b' and c' respectively.

Then for two triangles to be similar we have:

`(a)/(a')=(b)/(b')=(c)/(c')`

Here we have:

Juan drew a right triangle with leg length of 6 centimeters and 8 centimeters .

Now we will check in each of the options whose ratio are equal:

A. 9 centimeters and 16 centimeters

`(6)/(9)=(2)/(3)`

and
`(8)/(16)=(1)/(2)`

As
`(2)/(3)\\eq (1)/(2)`

Hence, option: A is incorrect.

B. 18 cm and 24 centimeters

`(6)/(18)=(1)/(3)`

and
`(8)/(24)=(1)/(3)`

As both the ratios are equal.

Hence, option: B is correct.

C. 16 centimeters and 18 centimeters

`(6)/(16)=(3)/(8)`

and
`(8)/(18)=(4)/(9)`

As
`(3)/(8)\\eq (4)/(9)`

Hence, option: C is incorrect.

D. 3 centimeters and 5 centimeters

`(6)/(3)=(2)/(1)`

and
`(8)/(5)`

As
`(2)/(1)\\eq (8)/(5)`

Hence, option: D is incorrect.