Question

triangle abc has a perimeter of 36cm & a area of 30cm² find the radius of the circle

Explanation:

Step1: Recall the formula for the area of a triangle in terms of in - radius and perimeter

The formula for the area of a triangle \(A=\text{Area}\), perimeter \(P\), and in - radius \(r\) is \(A = r\times\frac{P}{2}\).

Step2: Rearrange the formula to solve for \(r\)

Given \(A = 30\space cm^{2}\) and \(P=36\space cm\). From \(A=r\times\frac{P}{2}\), we can solve for \(r\) as \(r=\frac{2A}{P}\).
Substitute \(A = 30\) and \(P = 36\) into the formula: \(r=\frac{2\times30}{36}\).
Simplify the fraction: \(r=\frac{60}{36}=\frac{5}{3}\approx1.67\space cm\).

Answer:

The radius of the circle (in - radius) is \(\frac{5}{3}\space cm\) or approximately \(1.67\space cm\)