Question

Triangle A has sides of lengths `1 3 ,1 4`, and `11`. Triangle B is similar to triangle A and has a side of length `4`. What are the possible lengths of the other two sides of triangle B?

Answer 1

Given Triangle A: `13, 14, 11`
Triangle B: `4,56/13,44/13`
Triangle B: `26/7, 4, 22/7`
Triangle B: `52/11, 56/11, 4`

Explanation:

Let triangle B have sides x, y, z then, use ratio and proportion to find the other sides.
If the first side of triangle B is x=4, find y, z

solve for y:

`y/14=4/13`

`y=14*4/13`

`y=56/13`
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solve for z:
`z/11=4/13`

`z=11*4/13`
`z=44/13`
Triangle B: `4, 56/13, 44/13`

the rest are the same for the other triangle B

if the second side of triangle B is y=4, find x and z

solve for x:
`x/13=4/14`
`x=13*4/14`
`x=26/7`

solve for z:
`z/11=4/14`
`z=11*4/14`
`z=22/7`

Triangle B:`26/7, 4, 22/7`
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If the third side of triangle B is z=4, find x and y
`x/13=4/11`
`x=13*4/11`
`x=52/11`

solve for y:

`y/14=4/11`

`y=14*4/11`
`y=56/11`

Triangle B:`52/11, 56/11, 4`

God bless....I hope the explanation is useful.