Triangles Test

Result

Triangles Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

For each of the following statements, mention T for true and F for false.

i. Sides of two similar triangles are in the ratio 2 : 1, so the areas of these triangles would be in ratio 6 : 1.
ii. Three sides of a right angled triangle are 20 cm, 99 cm and 102 cm.
iii. In triangle ABC, AB = 3 cm, BC = 4 cm, AC = 5 cm and ∠ACB = 90°.
iv. If two sides of two triangles are proportional, then the third side is also proportional and the triangles are similar.

A
i - F, ii - F, iii - F, iv - F

B
i - T, ii - F, iii - F, iv - T

C
i - F, ii - F, iii - F, iv - T

D
i - F, ii - F, iii - T, iv - T

Solution

i. If the sides of two similar triangles are in ratio 2 : 1, then the ratio of their areas would be 2² : 1² i.e 4 : 1.
Hence, i is false.

ii. If the triangle is a right angled triangle, then,
102² must be equal to 99² + 20²
102² = 10404
99² + 20² = 9801 + 400 = 10201
Hence, ii is false

iii. Sides of the triangle are 3 cm, 4 cm and 5 cm which makes Pythagorean triplet and hence, the triangle is right angled and AC = 5 cm is the hypotenuse as it is the largest side. Hence, ∠ACB cannot be a right angle.
Hence, iii is false.

iv. For a fixed value of two sides of a triangle, third side of the triangle can vary depending upon the angle between the other sides. Hence, if two sides of the triangles are proportional, the third side need not to be proportional.
Hence, iv is false.