Question

5. In Fig. 1, find the length of the third side of the triangle.
√14
18
Fig. 1​

Answer 1

Answer:

Length of third side= 4√2

Step-by-step explanation:

Let AC be third side and AB & BC be the two sides ....

By applying Pythagoras theorem ,

AC²= AB²+ BC²

AC²=(√14)²+(√18)²

AC²=14+18

AC²=32

AC=4√2

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Answer 2

Step-by-step explanation:

Given : Two sides of a right angled triangle are $\sqrt{14}$  and $\sqrt{18}$ .

To find : Length of third side of right angled triangle

Formula used : We use Pythagoras theorem to find the length of third side(H).

$H^{2} =P^{2} +B^{2}$

$H=\sqrt{P^{2} +B^{2}}$

P is the perpendicular, B is the base and H is the hypotenuse of right angled triangle.

• Calculation for Third side,

We have perpendicular(P) and base(B),

$P=\sqrt{14}$

$B=\sqrt{18}$

by using Pythagoras theorem we can find Hypotenuse (H).

$H=\sqrt{P^{2} +B^{2}}$

   $= \sqrt{(\sqrt{14} )^{2} +(\sqrt{18} )^{2} }$

   $= \sqrt{(14^{\frac{1}{2} } )^{2} +(18^{\frac{1}{2} })^{2} }$

   $=\sqrt{14+18}$

   $=\sqrt{32}$

We can write 32 as $16*2=32$

   $=\sqrt{16*2}$

and as we know $\sqrt{16} =4$,

   $=4\sqrt{2}$

So the length of third side of triangle is $4\sqrt{2}$ .