the perimeter of a triangle is 30cm and the circumference of its incircle is 88cm the area of - Maths - Areas Related to Circles

Question

the perimeter of a triangle is 30cm and the circumference of its
incircle is 88cm the area of the triangle

Aakash Sharma · Accepted Answer

Given: Perimeter of âˆ†ABC = 30 cm â‡’AB + BC + AC = 30 cm (1) and circumference of incircle = 88 cm â‡’ 2Ï€ radius = 88 cm $\Rightarrow 2 \times \frac{22}{7} \times radius = 88 cm \Rightarrow Radius = \frac{88 \times 7}{44} cm = 14 cm$ Thus radius = OP = OQ = OR = 14 cm (2) we know that radius of circle is perpendicular to the tangent of the point of contact â‡’ OP âŠ¥ AB, OQ âŠ¥ BC, OR âŠ¥ AC Now Area (âˆ†ABC) = Area(AOB) + Area (BOC) + Area (AOC) $= \frac{1}{2} \times OP × AB + \frac{1}{2} \times OQ × BC + \frac{1}{2} \times OR × AC = \frac{1}{2} Radius (AB + BC + AC) (from (2)) = \frac{1}{2} \times 14 cm × 30 cm (from (1)) = 210 {cm}^{2}$

the perimeter of a triangle is 30cm and the circumference of its incircle is 88cm . the area of the triangle