Question #187677

The triangle ABC is right-angled with a right angle at C. The height CD has a length of 5 units of length (D lies on the side AB), and the distance AD ​​has a length of 7 units of length. Determine and state the length of the hypotenuse.


1
Expert's answer
2021-05-07T11:56:01-0400

According to given data:

Let x= remaining part of hypothenuse

b= base and

p= perpendicular




as CD is height of triangle

So, CD will be perpendicular


Now, In triangle ADC

Using Pythagoras Theorem

72+52=p2p=747^2+5^2=p^2\\\Rightarrow p=\sqrt{74}


Now in triangle BDC

Using Pythagoras Theorem

x2+52=b2x^2+5^2=b^2


In triangle ABC

Applying Pythagoras Theorem

p2+b2=(7+x)2(74)2+x2+25=(7+x)2p^2+b^2=(7+x)^2\\(\sqrt{74})^2+x^2+25=(7+x)^2


Solving Further

x2+74+25=49+x2+14xx=5014=3.57 unitsx^2+74+25=49+x^2+14x\\x=\dfrac{50}{14}=3.57 \ units


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