Triangle CAB (angle C = 90 degrees) from angle C draw the height to the hypotenuse AB Side AC = 15 cm

| September 2, 2021 | education

Triangle CAB (angle C = 90 degrees) from angle C draw the height to the hypotenuse AB Side AC = 15 cm, projection AD = 9 cm. How can I find the perimeter and area of the triangle?

From the right-angled triangle ACD, according to the Pythagorean theorem, we determine the length of the leg CD.

CD ^ 2 = AC ^ 2 = AD ^ 2 = 15 ^ 2 – 9 ^ 2 = 225 – 81 = 144.

СD = 12 cm.

The height BD is drawn from the top of the right angle, then its length is equal to the square root of the product of the segments by which this height divides the base of the AC.

CD = √AD * BD.

CD ^ 2 = AD * BD.

144 = 9 * BD.

ВD = 144/9 = 16 cm.

Then the side AB = AD + BD = 9 + 16 = 25 cm.

Then the area of ​​the triangle will be equal to: Savs = AB * CD / 2 = 25 * 12/2 = 150 cm2.

In a right-angled triangle ABC, we determine the length of the leg CB.

CB ^ 2 = AB ^ 2 – AC ^ 2 = 25 ^ 2 – 15 ^ 2 = 625 – 225 = 400.

CB = 20 cm.

Then Ravs = 20 + 25 + 15 = 60 cm.

Answer: The area of ​​the triangle is 150 cm2, the perimeter is 60 cm.



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