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The area and perimeter of a right triangle from median and side

Posted January 11th, 2008 by nikimiki
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In triangle ABC, angle B = 90 degree and D is the mid point of AC. If AB=20cm and BD=14.5cm, find the area and perimeter of the triangle.

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Comments

answer

On January 12th, 2008 Isoscel says:

Because B = 90 and D is the middle of AC we have:
BD = AD = DC

so:
$ AC = AD + DC = 2 \cdot BD = 2 \cdot 14.5 = 29 $

From the Pythagorean Theorem we have:
$ BC^2 = AC^2 - AB^2 $
$ BC^2 = 29^2 - 20^2 = 841 - 400 = 441 = 21^2 $
$ BC^2 = 21^2 $
because BC > 0
BC = 21

so:

$$Area(ABC) = \frac{AB \cdot BC}{2} = \frac{20 \cdot 21}{2} = 210$$
$$Perimeter(ABC) = AB + BC + CA = 20 + 21 + 29 = 70$$

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