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Any help would be appreciated. Thank you!

Any help would be appreciated. Thank you!-example-1
User Henryyao
by
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1 Answer

7 votes

Answer:

Area
=62.5√(6) square units


AB=5√(15) units


BC=5√(10) units

Explanation:

In a right triangle the altitude drawn to the hypotenuse is the geometric mean of the segments at which this altitude divides the hypotenuse.

So,


BD^2=15\cdot 10\\ \\BD^2=150\\ \\BD=√(150)=5√(6)\ units

a. The area of the triangle ABC is


A_(ABC)=(1)/(2)\cdot BD\cdot AC=(1)/(2)\cdot 5√(6)\cdot (15+10)=(125√(6))/(2)=62.5√(6)\ un^2.

b. The legs of the right triangle are geometric means of the segment adjacent to this leg and the hypotenuse, so


AB^2=AD\cdot AC=15\cdot 25\Rightarrow AB=5√(15)\ units\\ \\BC^2=CD\cdot AC=10\cdot 25\Rightarrow BC=5√(10)\ units

User Omid Shariati
by
7.8k points

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