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

△KJI is similar to  △GJH because all three pairs of corresponding angles are congruent.

One pair of corresponding side lengths is KJ and GJ .Together they form the fraction KJ / GJ

An other pair of corresponding side lengths is IK and HG. Together they form the fraction IK / HG .

In both fractions, the numerator comes from △KJI  and the denominator comes from △GJH Since the triangles are similar, you can use the fractions to set up a proportion and solve for r.

KJ / GJ = IK / HG

3 / 6 = 4 / r Plug in the side lengths

3 / 6 (6r) = 4 / r (6r) Multiply both sides by 6r

3 r = 4 . 6 Simplify

3r = 24 Simplify

3r ÷ 3 = 24 ÷ 3 Divide both sides by 3

r = 8

The missing length is 8 metres.

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

△GHD ~ △ EFD means that △GHD is similar to △ EFD

One pair of corresponding side lengths is DG and DE. Together they form the fraction DG / DE .

Another pair of corresponding side lengths is GH and EF. Together they form the fraction GH / EF .

In both fractions, the numerator comes from △GHD and the denominator comes from △ EFD .Since the triangles are similar, you can use the fractions to set up a proportion and solve for w.

DG / DE = GH / EF

4 / 8 = 2 / w Plug in the side lengths

4 / 8 (8w) = 2 / w (8w) Multiply both sides by 8w

4 w = 2 . 8 Simplify

4w = 16 Simplify

4w ÷ 4 = 16 ÷ 4 Divide both sides by 4

w = 4

The missing length is 4 metres.

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

△IJK is similar to  △MJL  because all three pairs of corresponding angles are congruent.

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

Another pair of corresponding side lengths is LM and KI. Together they form the fraction LM / KI .

In both fractions, the numerator comes from △MJL and the denominator comes from △IJK .Since the triangles are similar, you can use the fractions to set up a proportion and solve for K.

MJ / IJ = LM / KI

6 / 3 = 8 / K Plug in the side lengths

6 / 3 (3k) = 8 / k (3k) Multiply both sides by 3k

6 k = 8 . 3 Simplify

6k = 24 Simplify

6k ÷ 6 = 24 ÷ 6 Divide both sides by 6

k = 4

The missing length is 4 metres.