TRIANGLES

If △ ABC ~ △ DEF such that AB = 12 cm and DE = 14 cm. Find the ratio of areas of △ ABC and △ DEF.
1. 49/9
2. 36/9
3. 49/16
4. 25/49
D and E are points on the sides AB and AC respectively of a △ABC such that DE || BC. Which of the following statement is true?
i.△ ADE ~ △ ABC
ii.(area of △ ADE/ area of △ ABC) = (AD²/AB²)
iii.(area of △ ADE/ area of △ ABC)= (AB2/ AD2)
1. only (iii)
2. only (i)
3. only (i) and (ii)
4. All (i) , (ii) and (iii)
In the figure, PB and QA are perpendicular to segment AB. If OA = 5 cm, PO = 7cm and area (ΔQOA) = 150 cm², find the area of ΔPOB.
1. 233cm²
2. 294cm²
3. 300cm²
4. 420cm²
Two isosceles triangles have equal angles and their areas are in the ratio 16: 25. The ratio of corresponding heights is:
1. 4:5
2. 5:4
3. 3:2
4. 5:7
In △ABC, AB = 3 and, AC = 4 cm and AD is the bisector of ∠A. Then, BD : DC is —
1. 9: 16
2. 4:3
3. 3:4
4. 16: 9
ABCD is a parallelogram with diagonal AC If a line XY is drawn such that XY ∥ AB.
BX/XC=?
1. AY/AC
2. DZ/AZ
3. AZ/ZD
4. AC/AY
In ABC, Given that DE//BC, D is the midpoint of AB and E is a midpoint of AC.

The ratio AE: EC is ____.
1. 1: 3
2. 1: 1
3. 2: 1
4. 1: 2
In ΔABC, AC = 15 cm and DE || BC. If AB/AD=3, Find EC.
1. 5cm
2. 10cm
3. 2.5cm
4. 9cm
△ ABC is an acute angled triangle. DE is drawn parallel to BC as shown. Which of the following are always true?
i) △ ABC ∼ △ ADE

ii) AD/BD= AE/EC

iii) DE= BC/2
1. Only (i)
2. (i) and (ii) only
3. (i), (ii) and (iii)
4. (ii) and (iii) only
Which of the following is true?
1. EC/AC=AD/DE
2. BC/BD=CE/DE
3. AB/AD=BC/DE
4. All of the Above
If in △ CAB and △ FED, AB/ EF=BC/FD=AC/ED, then:
1. △ ABC∼△ DEF
2. △ CAB∼△ DEF
3. △ ABC∼△ EFD
4. △ CAB∼△ EFD
A tower of height 24m casts a shadow 50m and at the same time, a girl of height 1.8m casts a shadow. Find the length of the shadow of girl.
1. 3.75m
2. 3.5m
3. 3.25m
4. 3m
In the adjoining figure, if BC = a, AC = b, AB = c and ∠CAB = 120°, then the correct relation is-
1. a² = b² + c² – bc
2. a² = b² + c² + bc
3. a² = b² + c² – 2bc
4. a² = b² + c² + 2bc
If the distance between the top of two trees 20 m and 28 m tall is 17 m, then the horizontal distance between the trees is
1. 11m
2. 31m
3. 15m
4. 9m
In the figure △ABC is a right angled triangle with right angle at B. BD is perpendicular to AC. Then which of the following options will hold true?
1. AD²=DC×AC
2. AB²=AD×AC
3. AB²=AD×DC
4. AB²=DC²+AD²
In a right △ABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does not give the ratio of the areas of △ABD and △ACB?
1. (AB/AC)²
2. (AC/AB)²
3. (AB/AD)²
4. (BD/CB)²
△ ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm.△ DEF is similar to △ABC. If EF = 4 cm, then the perimeter of △DEF is –
1. 7.5cm
2. 15cm
3. 30cm
4. 22.5cm
In △ ABC and △ DEF, ∠A = ∠E = 40∘ and AB/ED=AC/EF. Find ∠B if ∠F is 65°
1. 85°
2. 75°
3. 35°
4. 65°
The ratio of the corresponding sides of two similar triangles is 1: 3. The ratio of their corresponding heights is _________
1. 1: 3
2. 3: 1
3. 1: 9
4. 9: 1
If Δ ABC and Δ DEF are similar such that 2AB = DE and BC = 8 cm, then Find EF
1. 16cm
2. 12cm
3. 8cm
4. 4cm
D and E are respectively the midpoints on the sides AB and AC of a triangle ABC and BC = 6 cm. If DE || BC, then the length of DE (in cm) is
1. 2.5
2. 3
3. 5
4. 6
In triangle PQR, if PQ = 6 cm, PR = 8 cm, QS = 3 cm, and PS is the bisector of angle QPR, what is the length of SR?
1. 2
2. 4
3. 6
4. 8

TRIANGLES

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