Practice Questions for Geometry - Triangles

1. PE 3 - Triangles | Geometry - Triangles

In the figure given below, if DE || FG || BC. Find AD : DF : FB?

(a)
1 : (√2 - 1) : (√3 - 1)
(b)
1 : √2 : √3
(c)
1 : 2 : 3
(d)
1 : (√2 - 1) : (√3 - √2)

2. PE 3 - Triangles | Geometry - Triangles

Length of the sides of a triangle are a, b and c. If a² + b² + c² = ab + bc + ca, then the triangle is

(a)
Scalene
(b)
Isosceles
(c)
Equilateral
(d)
Cannot be determined

3. PE 3 - Triangles | Geometry - Triangles

What is the highest possible area of a right triangle whose circumradius is 3 cm (in cm²)?

(a)
9
(b)
10
(c)
11
(d)
12

4. PE 3 - Triangles | Geometry - Triangles

In the figure given below, ABC is an equilateral triangle. If the area of bigger circle is 1386 cm², then what is the area (in cm²) of smaller circle. [π = 22/7]

(a)
144
(b)
154
(c)
288
(d)
462

5. PE 3 - Triangles | Geometry - Triangles

The two sides of a triangle are 10 and 5 cm. Find the shortest side of the if area of the triangle is 20 cm².

(a)
√65
(b)
√60
(c)
4
(d)
√80

6. PE 3 - Triangles | Geometry - Triangles

AB and BC are sides with integral length. If the length of side AC is 17 cm then find the possible value of the ratio of areas of triangle ABC and triangle BCD. (Given that angles B, C and E are all right angles).

(a) $\frac{64}{225}$
(b) $\frac{15}{8}$
(c) $\frac{225}{64}$
(d)
Both (a) and (c)

7. PE 3 - Triangles | Geometry - Triangles

PQR is a right angled triangle with PQ = 9 units and QR = 12 units. If ABCQ is a square, find its area?

(a)
20.75
(b)
31.33
(c)
26.45
(d)
25.67

8. PE 3 - Triangles | Geometry - Triangles

In a right triangle ABC, right angled at vertex B, side opposite angle A, B and C are a, b and c respectively. If r is in-radius and R is the circumradius of the triangle ABC, the 2(R + r) equals

(a)
a + b + c
(b)
a + b
(c)
b + c
(d)
c + a
(e)
None of these

9. PE 3 - Triangles | Geometry - Triangles

In ΔABC, AD and CE are the two medians drawn from A and C respectively, meeting BC and AB at D and E respectivley. AD and CE intersect at O. DF is drawn parallel to CE and meets AB at F. If area of ΔCOD is 16 cm², what is the area of quadrilateral DOEF?

(a)
48
(b)
12
(c)
20
(d)
16
(e)
36

10. PE 3 - Triangles | Geometry - Triangles

∆EFG is an isosceles triangle such that EF = EG. Angle bisector of ∠FEG intersects FG at Q. QR and PR are perpendiculars drawn from Q to EG and EF respectively intersecting them at points R and P respectively. Find the value of EP × EF, given that ER = 21 and RG = 9.

(a)
224
(b)
189
(c)
360
(d)
630
(e)
Cannot be determined

PE 3 - Triangles | Geometry - Triangles

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