Question

If two sides of a triangle are 7cm and 2.5cm, the length of its third side cannot be …..

A) 4.6 cm B) 4.4 cm C) 5.2 cm D) 4.9 cm​

Answer 1

$\LARGE{ \underline{\underline{ \sf{Required \: answer:}}}}$

Here we will use triangles inequality to determine which among the following length of the third side is not possible.

According to Triangle inequality,

• Any side of a triangle is always greater than the difference of other two sides of triangle.

Length of sides given:

• 7 cm
• 2.5 cm

Difference between the two sides,

➛ 7 cm - 2.5 cm

➛ 4.5 cm

According to inequality the third side is never lesser than the 4.5 cm. Hence, 4.4 cm is not the possible length of the third side of the traingle. So, The correct option is:

$\Large{ \boxed{ \bf{ \red{Option \: B}}}}$

And we are done! :D

Explore more!!

• Another triangle inequality states that the sum of any two sides in a triangle is always greater than the third side of the ∆.

Answer 2

Step-by-step explanation:

Given :

• If two sides of a triangle are 7cm and 2.5cm,

To Find :

• the length of its third side cannot be

Solution :

Pythagoras' theorem :

• → In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

AB² + BC² = AC²

LET AB= 7 cm AND BC = 2.5cm

( 7 ²) + ( 2.5 ² ) = AC²

49 + 6.25 = AC²

55.25 = AC²

AC = √55.25

AC = 5.03

According to inequality the third side is never lesser than the 5.03 cm. Hence, 4.9 cm , 4.4 cm and 4.6 cm is not the possible length of the third side of the traingle. So, The correct option is:

Hence Answer is C) 5.2cm

More to know :

It states that the Hypotenuse² is equals to Perpendicular²+ Base².

• In other words, The square of Hypotenuse or side opposite to 90° is equals to the sum of its Perpendicular & Base sq, where Hypotaneous is largest side.