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3 years ago

If AC = 40, find the length of JK.

Mathematics

2 answers:

lesantik [10]3 years ago

8 0

Answer:

JK = 24

Step-by-step explanation:

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

$\frac{JK}{AC}$ = $\frac{BK}{BC}$ , substitute values

$\frac{JK}{40}$ = $\frac{3}{5}$ ( cross- multiply )

5JK = 120 ( divide both sides by 5 )

JK = 24

eduard3 years ago

8 0

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

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