IXL | Similar triangles and indirect measurement

Find z.

5 m

6 m

10 m

Write your answer as a whole number or a decimal. Do not round.

z = meters

ref_doc_title.

Learn with an example

question

Find k.

3 ft

5 ft

Write your answer as a whole number or a decimal. Do not round.

k = feet

key idea

The sides of similar triangles are proportional.

solution

The original diagram included a smaller triangle inside a larger triangle. Redraw them as separate triangles.

3 ft

5 ft

JIH is similar to

KIL because all three pairs of corresponding angles are congruent.

One
pair
of
corresponding
side
lengths
is
IJ
and
IK
.
Together
they
form
the
fraction
IJ
IK
.

Another
pair
of
corresponding
side
lengths
is
JH
and
KL
.
Together
they
form
the
fraction
JH
KL
.

In both fractions, the numerator comes from

JIH and the denominator comes from

KIL. Since the triangles are similar, you can use the fractions to set up a proportion and solve for k.

5 + 5

Plug in the side lengths

Simplify

(

)

(

)

Multiply both sides by 10k

Simplify

Divide both sides by 5

The missing length is 6 feet.

Looking for more? Try these:

Lesson: Similar triangles

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S.8Side lengths and angle measures of similar figures

Lesson: Similar triangles

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