The value of the unknown length is 24
<h3>How to determine the
unknown length?</h3>
Represent the unknown length with x.
So, we have the following equivalent ratio:
30 : 30 + x = 25 : 45
Express as fraction
30/30 + x = 25/45
Simplify the fraction
30/30 + x = 5/9
Cross multiply
150 + 5x = 270
Evaluate the like terms
5x = 120
Divide by 5
x = 24
Hence, the value of the unknown length is 24
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The length of the hypotenuse will be equal to H=122.25 when value of x=14.
<h3>What is pythagorean theorem?</h3>
Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal the square of the sum of the other two sides.
It is given that:
Value of x=14
The perpendicular is =6x+5=6x14+5=89
The base is =6x=84
So by using the Pythagorean theorem:-

Hence the value of hypotenuse will be H=122.25
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Answer:
D
Step-by-step explanation:
CD is an angle bisector and divides the opposite side into segments which are proportional to the other 2 sides, that is
=
, substitute values
=
( cross- multiply )
3x = 9 ( divide both sides by 3 )
x = 3 → D