Question

1.
Which of the following measures can form a triangle?
(a) 7 cm, 10 cm, 7 cm
(b) 3 cm, 3.5 cm, 8 cm
(c) 8 cm, 9 cm, 11 cm
(d) 2 cm, 2 cm, 4.5 cm
State whether the follo​

Answer 1

Answer:

Let the larger side be the hypotenuse and also using pythagoras theorm,

(i) In triangle ABC

\left(AC\right)^2\ =\ \left(AB\right)^2\ +\ \left(BC\right)^2

\left(6.5\right)^2\ =\ \left(6\right)^2\ +\ \left(2.5\right)^2

42.25\ =\ 36\ +\ 6.25

42.25\ =\ 42.25\

LHS = RHS

Therefore, given sides are of the right angled triangle.

(ii) In triangle ABC,

\left(AC\right)^2\ =\ \left(AB\right)^2\ +\ \left(BC\right)^2

\left(5\right)^2\ =\ \left(2\right)^2\ +\ \left(2\right)^2

25 = 4+4

25 = 8

LHS\ \ne RHS\

Therefore, the given sides are not of the right angled triangle.

(iii) In triangle ABC,

\left(AC\right)^2\ =\ \left(AB\right)^2\ +\ \left(BC\right)^2

\left(2.5\right)^2=\ \left(2\right)^2\ +\ \left(1.5\right)^2

6.25 = 4 +2.25

6.25 = 6.25

LHS = RHS

therefore, the given sides are of the right angled triangle.

Step-by-step explanation:

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