Question

Triangle ABC below has a right angle C and a height CD. (A height in a triangle connects its vertex and the opposite side, and is perpendicular to that side.) d If AC is 3 units long and BC is 4 units long, what is the length of CD?

Answer 1

Answer:

2.4 units

Step-by-step explanation:

This question can be solved using the principle of area of triangle

Area of triangle = 1/3(base* height)

given

AC = 3 unit

BC = 4 unit

length of hypotenuse is found by using formula = $\sqrt{a^2 + b^2}$

where a and b are sides of right angled triangle other than hypotenuse

therefore hypotenuse(AB) is = $\sqrt{3^2 + 4^2} = \sqrt{25} = 5$

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Area of triangle when height is 4 unit(BC) and base is 3 unit(AC)

= 1/3( 4 * 3) = 4 square unit

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Now given that there is another height CD  

CD is perpendicular drawn from point CD to side AB

If CD is height for the triangle then its corresponding base will be the side on which this perpendicular is dropped.

in this problem it is Side AB which hypotenuse with side length 5 unit as calculated above

now again finding area for same triangle with height CD and base AB

we can also say Area of triangle ABC = 1/3(CD * AB) = 1/3(CD * 5) ------------equation A

since triangle ABC has area 4 square unit

1/3(CD * 5)   = 4 square unit

CD = (4 * 3)/5 = 12/5 = 2.4 units

length of CD = 2.4 units