Question

The length of two sides of a right triangle are d/3 and d/4 where d>0 if one of these side is the hypotenuse what is the length of the third side of the triangle

Answer 1

Answer:

d/5

Step-by-step explanation:

(d/3)2+(d/4)=x2

d2/9+d2/16=x2

16d2+9d2/16*9=x2

so x=d/5

Answer 2

The third side of the triangle = $\frac{\sqrt{7} d}{12}$  

Given: The length of two sides of right angle triangle

= d/3 and d/4 where d>0  

One of these sides is Hypotenuse

To find: Length of 3rd side of triangle

Solution: Given that d/3 and d/4 are two sides

Note: In the Right angle triangle the longest side is the hypotenuse

From given data hypotenuse of triangle will be d/3  [ ∵ d/3> d/4]  

From pythagorean theorem

Hypotenuse² = side² + side²

⇒ side² = Hypotenuse² - side²  

⇒ side² = $(\frac{d}{3})^{2} -( \frac{d}{4})^{2}$

⇒ side² = $\frac{d^{2} }{9} - \frac{d^{2} }{16}$  

⇒ side²  $=\frac{16d^{2}- 9d^{2} }{144}$

⇒ side² = $\frac{7d^{2} }{144}$  

⇒ side =   $\sqrt{\frac{7d^{2} }{144}}$ = $\frac{\sqrt{7} d}{12}$  

Therefore, the third side of the triangle = $\frac{\sqrt{7} d}{12}$

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