Class 10 Areas of Similar Triangles — practice questions with answers
Geometry — Similarity · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. The ratio of areas of two similar triangles equals the ratio of the squares of their corresponding ____.
Asides
Bangles
Cperimeters cubed
Dheights added
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Answer: A) sides
By the Area Theorem, area ratio = (ratio of corresponding sides)², so it equals the ratio of squares of corresponding sides.
2. Two similar triangles have corresponding sides 10 cm and 14 cm. Find the ratio of their areas.
A25:49
B10:14
C5:7
D49:25
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Answer: A) 25:49
Side ratio = 10:14 = 5:7. Area ratio = (75)2 = 25:49.
3. Two similar triangular tiles cost Rs in proportion to their areas. The corresponding sides are 8 cm and 12 cm; the smaller tile costs Rs 80. Find the cost of the larger tile (in Rs).
A160
B200
C180
D360
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Answer: C) 180
Area ratio larger:smaller = (812)2=49. Larger cost = 80×49 = Rs 180.
4. A map is drawn to a scale in which 1 cm on the map represents 5 km on the ground. A triangular forest reserve appears on the map as a triangle of area 6 cm², similar in shape to the real reserve. Find the actual area of the reserve in km².
A30
B750
C150
D1.2
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Answer: C) 150
Lengths are multiplied by 5, so areas are multiplied by 52=25. Actual area = 6×25=150 km². Multiplying the area by 5 gives 30 km², the commonest slip; cubing the scale gives 750 km² and dividing by 5 gives 1.2 km².
5. Triangle ABC is similar to triangle PQR with area(ABC) : area(PQR) = 49 : 25. A student writes: 'So the perimeters are in the ratio 49 : 25, and the corresponding medians are in the ratio 2401 : 625.' Which single correction repairs both statements?
AThe perimeters are 49 : 25 but the medians are 7 : 5
BThe perimeters are 7 : 5 but the medians are 49 : 25
CBoth the perimeters and the medians are in the ratio 7 : 5
DThe perimeters are 2401 : 625 and the medians are 49 : 25
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Answer: C) Both the perimeters and the medians are in the ratio 7 : 5
A perimeter and a median are both LENGTHS, so each is in the same ratio as the corresponding sides: 2549=57. The student squared once too often at every stage, first treating the area ratio as a length ratio and then squaring that again for the medians.