Answer to Question #187677 in Geometry for Robin

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

"7^2+5^2=p^2\\\\\\Rightarrow p=\\sqrt{74}"


Now in triangle BDC

Using Pythagoras Theorem

"x^2+5^2=b^2"


In triangle ABC

Applying Pythagoras Theorem

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


Solving Further

"x^2+74+25=49+x^2+14x\\\\x=\\dfrac{50}{14}=3.57 \\ units"


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