Question
Download Solution PDFThe hypotenuse of a right angled triangle is 10 cm and the radius of the inscribed circle is 1 cm. The perimeter of the triangle in centimeter is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The hypotenuse of a right-angled triangle is 10 cm and the radius of the inscribed circle is 1 cm.
Concept used:
1. Inradius of a right-angled triangle can be given as r = (P + B – H) / 2 (where P = perpendicular, B = base, and H = Hypotenuse)
2. The perimeter of a triangle is the sum of all sides.
Calculation:
Let the length of the perpendicular and base of the triangle be P and B respectively.
According to the concept,
(P + B – 10) / 2 = 1
⇒ (P + B - 10) = 2
⇒ (P + B) = 12
Now, the perimeter of the triangle
⇒ (P + B + 10)
⇒ 12 + 10 = 22 cm
∴ The perimeter of the triangle is 22 cm.
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