Question

The length of two sides of a triangle are 10cm and 15cm . Between what two measures should the lenght of the third side lie?

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{The length of two sides of a triangle are 10 cm and 15 cm}$

$\underline{\textbf{To find:}}$

$\textsf{Between what two measures should the length of the}$

$\textsf{third side lie}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Concept used:}}$

$\textbf{The sum of lengths any two sides of a triangle is}$

$\textbf{greater than length of the third side}$

$\textsf{Let the length of the third side be 'x'}$

$\textsf{Here, we have two cases}$

$\mathsf{Case(i):}$

$\mathsf{10+15\,>\,x}$

$\mathsf{25\,>\,x}$

$\implies\boxed{\mathsf{x\,<\,25}}$

$\mathsf{Case(ii):}$

$\mathsf{10+x\,>\,15}$

$\mathsf{x\,>\,15-10}$

$\mathsf{x\,>\,5}$

$\implies\boxed{\mathsf{x\,>\,5}}$

$\textsf{Combining both the cases, we have}$

$\boxed{\mathsf{5\,<\,x\,<\,25}}$

$\underline{\textbf{Find more:}}$

If the ratio of sines of angles of a triangle is 1 : 1 : √2 then the ratio of square of the greatest side to sum of the squares of other two sides is

(a) 3 : 4

(b) 2 : 1

(c) 1 : 1

(d) 1 : 2

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Area of ​​a triangle formed by x-axis, y-axis and line x + y = 8 is ....... square unit

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