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The hypotenuse of right triangle is 52 centimeters long. The difference between the other two sides is 28 centimeters.

Find the missing sides. Use exact values.

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Answer:

The length of the perpendicular = 20 meters

The length of the base = 48 meters

Explanation:

The hypotenuse of the triangle = 52 meters

Let the Length of the perpendicular is = k meters

So, the length of the base = ( k + 28) m

Now, by PYTHAGORAS THEOREM , in a right angled triangle:


(BASE)^(2)   + (PERPENDICULAR)^(2)  =  (HYPOTENUSE)^(2)

⇒ Here,
(k)^(2) + (k +28) ^(2)  = (52)^(2)

Also, by Algebraic Identity:


(a+b) ^(2)  = a^(2) + b ^(2) + 2ab\\ \implies (k+28) ^(2)  = k^(2) + (28) ^(2) + 2(28)(k)\\

So, the equation becomes:


(k)^(2) +k^(2) + (28) ^(2) + 2(28)(k)  = (52)^(2)

or,
2k^(2)  + 784+ 56k = 2704\\\implies k^(2) + 28k - 960 = 0

or,
k^(2)  + 48k -20 k - 960 = 0

Solving the equation:

⇒ (k+48)(k-20) = 0 , or (k+48) = 0 , or (k-20) = 0

or, either k = -48 , or k = 20

As k is the length of the side, so k ≠ - 48, k = 20

Hence, the length of the perpendicular = k = 20 meters

and the length of the base is k + 28 = 48 meters

User Koayst
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