Question

In the figure below, find the exact value of x . (Do not approximate your answer.)

Answer 1

Answer:

The value of x is 9/4 i.e. 2.25

Answer 2

Answer:  [$x=2.25$]

Step-by-step explanation:

Given

• a right-angled triangle with hypotenuse (4 + x).
• The altitude drawn from the right-angle vertex on the hypotenuse intersects the hypotenuse perpendicularly and its length is 3.

To Find: The exact value of x.

Explanation:

To solve this question, let us name the given triangle as shown in the "Reference for Naming of Triangle.docx" attached hereby.

• Another thing we need to know about is the "Pythagorus Theorem"

        The Pythagorus theorem states that “In case of a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides”.

[For the figure, please refer to "Pythagorus Theroem.docx" attached hereby].

• Firstly, Triangle ADB is also a right-angled triangle with right-angle at D.

        Therefore, Base of Triangle ADB = BD = 4,

         Height of Triangle ADB = AD = 3,

         And, Hypotenuse of Triangle ADB = AB

• Using the Pythagorus Theorem, we get,

        $[(AD)^{2}+(BD)^{2}]=(AB)^{2}\\or,(AB)^{2}=[(3)^{2}+(4)^{2}]\\or,(AB)^{2}=[9+16]\\or,(AB)^{2}=25\\or, \sqrt{(AB)^{2}}=\sqrt{25}\\ or, AB = 25$

• Triangle ADC is also a right-angled triangle with right-angle at D.
•         Therefore, Base of Triangle ADC = DC = x,
•          Height of Triangle ADC = AD = 3,
•          And, Hypotenuse of Triangle ADC = AC
• Using the Pythagorus Theorem, we get,

        $[(DC)^{2}+(AD)^{2}]=(AC)^{2}\\or,(AC)^{2}=[(3)^{2}+(x)^{2}]\\or,(AC)^{2}=[9+x^{2} ]$

• Triangle ABC is also a right-angled triangle with right-angle at A.
•         Therefore, Base of Triangle ABC = AC,
•          Height of Triangle ABC = AB = 5,
•          And, Hypotenuse of Triangle ABC = BC = (4+x)
• Using the Pythagorus Theorem, we get,

        $[(AC)^{2}+(AB)^{2}]=(BC)^{2}\\or, (BC)^{2}=[(AC)^{2}+(AB)^{2}]\\or,(4+x)^{2}=[(9+x^{2} )+(5)^{2}]\\or, [4^{2} + (2*4*x) + x^{2}]=[9+x^{2} +25]\\or, [16 + 8x + x^{2}]=[(9+25) + x^{2}]\\or, [16 + 8x + x^{2}]=[34 + x^{2}]\\or, [16 + 8x + x^{2}]-[34 + x^{2}]=0\\or, (16-34)+8x+(x^{2}-x^{2})=0\\\\or, 8x-18=0\\or, 8x=18\\or, x=\frac{18}{8}\\or, x=\frac{9*2}{4*2}\\or, x=\frac{9}{4}\\or, x = 2.25$

If in a right-angled triangle lengths of sides forming right angle are 24 cm and 18 cm , then length of its hypotenuse is:

1️⃣ 24 cm

2️⃣ 30 cm

3️⃣ 15 cm

4️⃣ 18 cm​

https://brainly.in/question/47411723

If the two angles of a right angle triangle are in the ratio 2:3, then find the measure of each of these angles​.

https://brainly.in/question/13021499

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7978b417e247032bf3dcaa5b3e9951b2.docx

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