Find missing lengths in similar triangles
10th grade (Year 11 in England) · 16 questions · Common Core: HSG.SRT.B.5 · England: GCSE Foundation Geometry, GCSE Higher Geometry
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Question 1
In triangle ABC, D is on AB and E is on AC with DE parallel to BC. AD = 3 cm, DB = 4 cm and DE = 6 cm. Find BC.
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Question 2
Triangles ABC and PQR are similar, with AB matching PQ and BC matching QR. AB = 3 cm, PQ = 6 cm and BC = 6 cm. Find QR.
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Question 3
Ana is 1.8 m tall and casts a 2 m shadow. At the same moment a tree casts a 19 m shadow. How tall is the tree, to 1 decimal place?
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Question 4
In triangle ABC, D is on AB and E is on AC with DE parallel to BC. AD = 3 cm, DB = 8 cm and DE = 7 cm. Find BC to 1 decimal place.
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Question 5
Triangles ABC and PQR are similar, with AB matching PQ and BC matching QR. AB = 9 cm, PQ = 22.5 cm and BC = 6 cm. Find QR.
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Question 6
Jamal is 1.5 m tall and casts a 3 m shadow. At the same moment a tree casts a 12 m shadow. How tall is the tree, to 1 decimal place?
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Question 7
In triangle ABC, D is on AB and E is on AC with DE parallel to BC. AD = 8 cm, DB = 4 cm and DE = 4 cm. Find BC.
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Question 8
Triangles ABC and PQR are similar, with AB matching PQ and BC matching QR. AB = 3 cm, PQ = 9 cm and BC = 9 cm. Find QR.
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Question 9
Mateo is 1.2 m tall and casts a 1.2 m shadow. At the same moment a tree casts a 29 m shadow. How tall is the tree, to 1 decimal place?
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Question 10
In triangle ABC, D is on AB and E is on AC with DE parallel to BC. AD = 3 cm, DB = 9 cm and DE = 7 cm. Find BC.
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Question 11
Triangles ABC and PQR are similar, with AB matching PQ and BC matching QR. AB = 5 cm, PQ = 15 cm and BC = 4 cm. Find QR.
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Question 12
Grace is 1.6 m tall and casts a 2 m shadow. At the same moment a tree casts a 24 m shadow. How tall is the tree, to 1 decimal place?
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Question 13
In triangle ABC, D is on AB and E is on AC with DE parallel to BC. AD = 6 cm, DB = 3 cm and DE = 2 cm. Find BC.
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Question 14
Triangles ABC and PQR are similar, with AB matching PQ and BC matching QR. AB = 3 cm, PQ = 4.5 cm and BC = 4 cm. Find QR.
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Question 15
Ethan is 1.2 m tall and casts a 2.4 m shadow. At the same moment a tree casts a 25 m shadow. How tall is the tree, to 1 decimal place?
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Question 16
In triangle ABC, D is on AB and E is on AC with DE parallel to BC. AD = 8 cm, DB = 10 cm and DE = 8 cm. Find BC.
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