Area of a split right triangle

Level 1

Triangle A B C ABC has a right angle at C C . Point D D lies on hypotenuse A B AB such that C D CD is perpendicular to A B AB . If A D = 4 AD=4 and B D = 9 BD=9 , what is the area of the triangle?


The answer is 39.

Alexander Katz by Alexander Katz , 24, USA

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2 solutions

Biswajit Barik
Feb 13, 2017

First of all we find CD which is

6 then the area will be surely 1/2base*height

0 Helpful 0 Interesting 1 Brilliant 0 Confused
Lucky Narasimhan
Oct 27, 2017

Theorem CD2(square )=AD*BD

0 Helpful 0 Interesting 0 Brilliant 0 Confused

We easily can see that triangles BCD and ACD are similar. Letting altitude CD be 'x', we find 4/x = x/9. After some easy simplification, we can see that x = 6. Then, to find the area of the triangle, we multiply the length of altitude CD, 6, by the length of the hypotenuse AB, 4 + 9 = 13, and divide by 2 to get that the area is 39 for the triangle ABC as our final answer.

Noah Yared - 5 months, 2 weeks ago

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