Area of a right triangle is 54 cm. If one of its legs is 12 cm long, its perimeter is
(a) 18 cm
(b) 27 cm
(C) 36 cm
(d) 54 cm
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the perimeter of the right triangle is 36 cm
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- The area of a right triangle is 54 cm.
- One of its legs is 12 cm long.
- The perimeter of a right triangle.
We know, The area of a right triangle
➝ ½ × base × hieght
According to the question,
The area of a right triangle is 54 cm.
➝ 54 = ½ × base × hieght
➝ 54 = ½ × 12 × hieght
➝ 54 = 6 × hieght
➝ hieght = 54 / 6
➝ hieght = 9 cm
In a right angle Δ ABC,
AC² = AB² + BC²
➝ AC² = 12² + 9²
➝ AC² = 144 + 81
➝ AC² = 225
➝ AC = √225
➝ AC = 15 cm
We know, The perimeter of a triangle is a + b + c
➝ 12 + 9 + 15
➝ 27 + 9
➝ 36 cm
The perimeter of a right triangle is 36 cm .
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