IXL | Similar figures and indirect measurement

Find z.

4 ft

3 ft

6 ft

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

z = feet

ref_doc_title.

Learn with an example

question

Find z.

5 m

10 m

8 m

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

z = meters

key idea

The sides of similar triangles are proportional.

solution

The original diagram included a smaller triangle and a larger triangle. Redraw them as separate triangles with corresponding sides in the same color.

5 m

10 m

8 m

JKL is similar to

MKN because all three pairs of corresponding angles are congruent.

One
pair
of
corresponding
side
lengths
is
NM
and
LJ
.
Together
they
form
the
fraction
NM
LJ
.

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

In both fractions, the numerator comes from

MKN and the denominator comes from

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

Plug in the side lengths

(

)

(

)

Multiply both sides by 5z

Simplify

Divide both sides by 10

The missing length is 4 meters.

Looking for more? Try these:

Lesson: Similar triangles

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Teacher tools

Work it out

Not feeling ready yet? These can help:

FF.4Side lengths and angle measures of similar figures

Lesson: Similar triangles

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