Answer to Question #187677 in Geometry for Robin

Question

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.

Answer 1

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

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