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Worksheet: Proportions in Similar Triangles

Q1:

The ratio of the areas of two similar triangles is 9 1 0 0 . If the perimeter of the larger triangle is 129, what is the perimeter of the smaller one?

Q2:

The perimeter of the one of two similar triangles is 31.5 cm, and the side lengths of the other are 9 cm, 2 cm, and 10 cm. Find the length of the longest side of the first triangle rounded to two decimal places.

Q3:

In the diagram, β–³ 𝐷 𝐸 𝐹 ∼ β–³ 𝐢 𝐡 𝐹 and the perimeter of β–³ 𝐢 𝐡 𝐹 is 104. Given that 𝐷 𝐹 = 2 1 and 𝐹 𝐢 = 2 8 , find the perimeter of β–³ 𝐷 𝐸 𝐹 .

Q4:

In the diagram, β–³ 𝐷 𝐸 𝐹 ∼ β–³ 𝐢 𝐡 𝐹 and the perimeter of β–³ 𝐢 𝐡 𝐹 is 178. Given that 𝐷 𝐹 = 2 5 and 𝐹 𝐢 = 4 0 , find the perimeter of β–³ 𝐷 𝐸 𝐹 .

Q5:

Suppose β–³ 𝐴 𝐡 𝐢 ∼ β–³ 𝐷 𝐸 𝐹 . If the ratio of the perimeter of β–³ 𝐴 𝐡 𝐢 to that of β–³ 𝐷 𝐸 𝐹 is 2 5 , and the sum of their areas is 64 cm2, determine their areas rounded to the nearest hundredth.

  • Aarea of β–³ 𝐴 𝐡 𝐢 = 2 5 . 6 0 c m 2 , area of β–³ 𝐷 𝐸 𝐹 = 3 8 . 4 0 c m 2
  • Barea of β–³ 𝐴 𝐡 𝐢 = 1 8 . 2 9 c m 2 , area of β–³ 𝐷 𝐸 𝐹 = 4 5 . 7 1 c m 2
  • Carea of β–³ 𝐴 𝐡 𝐢 = 1 0 . 2 4 c m 2 , area of β–³ 𝐷 𝐸 𝐹 = 5 3 . 7 6 c m 2
  • Darea of β–³ 𝐴 𝐡 𝐢 = 8 . 8 3 c m 2 , area of β–³ 𝐷 𝐸 𝐹 = 5 5 . 1 7 c m 2
  • Earea of β–³ 𝐴 𝐡 𝐢 = 4 . 4 1 c m 2 , area of β–³ 𝐷 𝐸 𝐹 = 7 . 0 0 c m 2

Q6:

Given that β–³ 𝐴 𝐡 𝐢 and β–³ 𝑋 π‘Œ 𝑍 are similar triangles, 𝐴 𝐡 𝑋 π‘Œ = 5 8 , and the perimeter of β–³ 𝐴 𝐡 𝐢 is 28.1 cm, find the perimeter of β–³ 𝑋 π‘Œ 𝑍 to the nearest tenth.

Q7:

The ratio between the perimeters of two similar triangles is : . Given that the difference between their areas is 288 cm2, calculate the area of each triangle.

  • A 216 cm2, 72 cm2
  • B 96 cm2, 192 cm2
  • C 36 cm2, 324 cm2

Q8:

The sum of the areas of two similar triangles is 740 cm2. Given that the ratio between their perimeters is 8 ∢ 1 1 , find the areas of both triangles.

  • A 2 713 cm2, 312 cm2
  • B 1 018 cm2, 202 cm2
  • C 256 cm2, 484 cm2

Q9:

The figure shows triangles 𝐴 𝐡 𝐢 and 𝐢 𝐷 𝐸 , where 𝐢 lies on 𝐴 𝐷 and 𝐡 𝐸 .

Work out the value of π‘₯ .

Work out the value of 𝑦 .

Work out the perimeter of β–³ 𝐴 𝐡 𝐢 .

Q10:

𝐴 𝐡 𝐢 and 𝐷 𝐸 𝐹 are similar triangles. Suppose that the ratio of the area of β–³ 𝐴 𝐡 𝐢 to the area of β–³ 𝐷 𝐸 𝐹 is 1 4 , the perimeter of β–³ 𝐴 𝐡 𝐢 is 230, and 𝐸 𝐹 = 7 6 . Determine the perimeter of β–³ 𝐷 𝐸 𝐹 and 𝐡 𝐢 .

  • A perimeter of β–³ 𝐷 𝐸 𝐹 = 1 1 5 , 𝐡 𝐢 = 1 5 2
  • B perimeter of β–³ 𝐷 𝐸 𝐹 = 4 6 0 , 𝐡 𝐢 = 1 9
  • C perimeter of β–³ 𝐷 𝐸 𝐹 = 5 7 . 5 , 𝐡 𝐢 = 3 8
  • D perimeter of β–³ 𝐷 𝐸 𝐹 = 4 6 0 , 𝐡 𝐢 = 3 8
  • E perimeter of β–³ 𝐷 𝐸 𝐹 = 9 2 0 , 𝐡 𝐢 = 3 8

Q11:

𝐴 𝐡 𝐢 is a triangle whose side lengths are 43 cm, 39 cm, and 54 cm. If β–³ 𝐴 𝐡 𝐢 ∼ β–³ 𝑍 π‘Œ 𝐿 and the perimeter of β–³ 𝑍 π‘Œ 𝐿 = 6 8 c m , find the side lengths of β–³ 𝑍 π‘Œ 𝐿 .

  • A 86 cm, 78 cm, 108 cm
  • B 5.375 cm, 4.875 cm, 6.75 cm
  • C 43 cm, 39 cm, 54 cm
  • D 21.5 cm, 19.5 cm, 27 cm

Q12:

𝐴 𝐡 𝐢 is a triangle whose side lengths are 30 cm, 39 cm, and 48 cm. If β–³ 𝐴 𝐡 𝐢 ∼ β–³ 𝑍 π‘Œ 𝐿 and the perimeter of β–³ 𝑍 π‘Œ 𝐿 = 4 6 . 8 c m , find the side lengths of β–³ 𝑍 π‘Œ 𝐿 .

  • A 75 cm, 97.5 cm, 120 cm
  • B 1.92 cm, 2.496 cm, 372 cm
  • C 30 cm, 39 cm, 48 cm
  • D 12 cm, 15.6 cm, 19.2 cm
  • E 2.4 cm, 3.12 cm, 3.84 cm

Q13:

If 𝐴 𝐸 = 1 3 . 6 c m and 𝐷 𝐸 = 1 3 . 7 c m , find the perimeter of β–³ 𝐸 𝐡 𝐢 .

Q14:

The ratio between the lengths of two corresponding sides of two similar polygons is 2 ∢ 9 . If the perimeter of the smaller polygon is 68 cm, determine the perimeter of the bigger one rounded to two decimal places.

Q15:

Find the perimeter of β–³ 𝐴 𝐡 𝐢 .

Q16:

Given that the triangles shown are similar, what is the perimeter of the larger one?

Q17:

One of two similar triangles has a perimeter of 51 cm, while the side lengths of the other are 87.5 cm, 49 cm, and 42 cm. Find the length of the longest side in the first triangle.

Q18:

The figure shows triangle 𝐴 𝐡 𝐢 .

Work out the value of π‘₯ .

Work out the value of 𝑦 .

Work out the perimeter of β–³ 𝐴 𝐡 𝐢 .

Q19:

Complete the following: The ratio between the two perimeters of two similar triangles is equal to the ratio between .

  • Atheir areas
  • Btheir angles
  • Ctheir sides squared
  • Dtheir corresponding sides
  • Etheir sides cubed