The height of the triangle is 12 and divides the side equal to 21, in a ratio of 16: 5, find the perimeter of this triangle.
| July 6, 2021 | education
Let the length of the segment AH = 5 * X cm, then, by condition, CH = 16 * X cm.
Base AC = AH + CH = 21 cm, then:
5 * X + 16 * X = 21.
21 * X = 21.
X = 1.
AH = 1 * 5 = 5 cm.
CH = 1 * 16 = 16 cm.
From the right-angled triangle ABN, we determine the length of the hypotenuse AB.
AB ^ 2 = BH ^ 2 + AH ^ 2 = 144 + 25 = 169.
AB = 13 cm.
Similarly, from the triangle BCH: BC ^ 2 = CH ^ 2 + BH ^ 2 = 256 + 144 = 400.
BC = 20 cm.
Determine the perimeter of the triangle ACB.
Ravs = AB + BC + AC = 13 + 20 + 21 = 54 cm.
Answer: The perimeter of the triangle is 54 cm.
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