Question

the length of two sides of a triangle are 4,5?write all the possible lengths of third side​

Answer 1

How to find the third side?

Sum = 4+5 =9

Difference 5-4=1

The third side should be a number between 9 and 1

So it can be any number between 1 and 9

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Hope this is useful

Answer 2

$\Large{\underline{\underline{\bf{Solution :}}}}$

We have given two sides of triangle as 4, 5. We have to find all the possible lengths of tge third side.

We know that,

$\Large{\implies{\boxed{\boxed{\sf{(H)^2 = (B)^2 + (P)^2}}}}}$

Where,

B is Base

P is Perpendicular

H is Hypotenuse

$\rule{150}{2}$

Let Hypotenuse be 5 and perpendicular be 4.

We get,

$\sf{→(5)^2 = (4)^2 + (Base)^2} \\ \\ \sf{→(Base)^2 = 25 - 16} \\ \\ \sf{→(Base)^2 = 9} \\ \\ \sf{→B = \pm 3}$

$\rule{150}{2}$

Now, Let 4 be Hypotenuse and 5 be perpendicular.

$\sf{→ (4)^2 = (5)^2 + (Base)^2} \\ \\ \sf{→(Base)^2 = 16 - 25} \\ \\ \sf{→(Base)^2 = -9} \\ \\ \sf{→Base = \sqrt{-9}}$

$\rule{150}{2}$

Now, 5 be Base and 4 be perpendicular.

$\sf{(Hypotenuse)^2 = (5)^2 + (4)^2} \\ \\ \sf{→(Hypotenuse)^2 = 25 + 16} \\ \\ \sf{→ (Hypotenuse)^2 = 41} \\ \\ \sf{→Hypotenuse = \sqrt{42}}$

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