Answer to Question #188758 in Geometry for Ahmad

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. Briefly explain each step

Answer 1

According to given information,

we can draw diagram as follows:

with some variables x, b and p.

as CD is height so CD is perpendicular to AB.

NOW,

applying Pythagoras theorem in triangle ADC,

$7^2+5^2=p^2$

$p=\sqrt{74}$ ............................(1)

applying Pythagoras theorem in triangle BDC,

$x^2+5^2=b^2$ ...............(2)

applying Pythagoras theorem in triangle ACB ,using (1),

$74+b^2=(7+x)^2$ ...........................(3)

eliminating b from eqn. (2) and(3)...

we get,

$x^2 +25=(7+x)^2-74$

$\boxed {x={50\over 14}}$

therefore,

length of hypotenuse is,

=$x+7$

$={50\over 14} +7$

$\boxed{ = 10.57 \ unit}$