Question

If AC = 40, find the length of JK.

Answer 1

the triangles are all similar, because they have proportional sides and equal angles.

if you assume the smallest, equal part of side to be x

the biggest triangle has "5 parts" so BC=5x and BK has 3 parts so BK=3x .

since they're similar, ratio of their corresponding sides is constant or equal.

`{BK\over BC}={JK \over AC}`

BK/BC=3/5

and AC=40

so JK = 40*3/5=24

Answer 2

JK = 24

Explanation:

Δ BKJ and Δ BCA are similar triangles and ratios of corresponding sides are equal, that is

`(JK)/(AC)` =
`(BK)/(BC)` , substitute values

`(JK)/(40)` =
`(3)/(5)` ( cross- multiply )

5JK = 120 ( divide both sides by 5 )

JK = 24