Similar Shapes (Lengths) worksheet
10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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4 marks
Rectangle \(A\) and rectangle \(B\) are similar.
(a)Work out the scale factor of the enlargement from rectangle \(A\) to rectangle \(B\).
(b)Work out the length marked \(x\).
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3 marks
Triangle \(ABC\) is similar to triangle \(PQR\), so that \(A\) corresponds to \(P\), \(B\) to \(Q\) and \(C\) to \(R\).
Calculate the length of \(QR\).
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3 marks
Amara has a photograph that is \(9\) cm wide and \(6\) cm high.
She enlarges it. The enlarged photograph is \(12\) cm wide, and it is similar to the original.
Find the height of the enlarged photograph.
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3 marks
One afternoon Rosa measures the shadows in a park.
A bollard \(1\) m tall casts a shadow \(3\) m long. At the same moment a flagpole casts a shadow \(18\) m long.
The sun's rays are parallel, so the two triangles below are similar.
Calculate the height of the flagpole.
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4 marks
Triangle \(ABC\) is similar to triangle \(PQR\), so that \(A\) corresponds to \(P\), \(B\) to \(Q\) and \(C\) to \(R\).
\(AB = 7\) cm and \(PQ = 14\) cm.
Marcus says:
"The scale factor of the enlargement from \(ABC\) to \(PQR\) is \(7\), because \(14 - 7 = 7\)."
(a)Explain why Marcus is wrong.
(b)Write down the correct scale factor.
(c)\(BC = 4\) cm. Work out the length of \(QR\).
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6 marks
Triangle \(ABC\) is similar to triangle \(PQR\), so that \(A\) corresponds to \(P\), \(B\) to \(Q\) and \(C\) to \(R\).
(a)Write down, as a fraction in its simplest form, the scale factor of the enlargement from triangle \(ABC\) to triangle \(PQR\).
(b)Find the length marked \(y\).
(c)Find the length marked \(x\).
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4 marks
Rectangle \(A\) and rectangle \(B\) are similar.
(a)Work out the scale factor of the enlargement from rectangle \(A\) to rectangle \(B\).
(b)Work out the length marked \(x\).
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3 marks
Triangle \(ABC\) is similar to triangle \(PQR\), so that \(A\) corresponds to \(P\), \(B\) to \(Q\) and \(C\) to \(R\).
Find the length of \(QR\).
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3 marks
Priya has a photograph that is \(6\) cm wide and \(9\) cm high.
She enlarges it. The enlarged photograph is \(14\) cm wide, and it is similar to the original.
Work out the height of the enlarged photograph.
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3 marks
One afternoon Priya measures the shadows in a park.
A bollard \(2\) m tall casts a shadow \(5\) m long. At the same moment a tree casts a shadow \(25\) m long.
The sun's rays are parallel, so the two triangles below are similar.
Work out the height of the tree.
Answers
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(a) \(3\)
(b) \(15\ \text{cm}\) - \(24\ \text{cm}\)
- \(8\ \text{cm}\)
- \(6\ \text{m}\)
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(a) A scale factor multiplies rather than adds, so it comes from dividing corresponding lengths: \(14 \div 7 = 2\), not \(14 - 7 = 7\).
(b) \(2\)
(c) \(8\ \text{cm}\) -
(a) \(\frac{3}{4}\)
(b) \(24\ \text{cm}\)
(c) \(28\ \text{cm}\) -
(a) \(4\)
(b) \(16\ \text{cm}\) - \(8\ \text{cm}\)
- \(21\ \text{cm}\)
- \(10\ \text{m}\)