# Ratio of Similar Triangles

by Ghazala
(Karachi, Pakitstan)

Similar Triangles - Ratio of Areas

Find out the ratio of area of Triangle ARB and BRC ?

### Comments for Ratio of Similar Triangles

 Oct 31, 2011 Ratio of Area of Triangles by: Staff Question: by Ghazala (Karachi, Pakistan) Find out the ratio of area of Triangle ARB and BRC ? Answer: I have calculated the ratio of the two areas below. However, it is worth noting that △ ARB and △ BRC are NOT SIMILAR TRIANGLES. To be similar triangles, the corresponding angles of each triangle must be the same. △ ARB is a Right Triangle (one of its interior angles is 90°) and △ BRC is an Obtuse Triangle (one of its interior angles is more than 90°) The formula for the area of a triangle is: A = (1/2)*b*h h = vertical height b = base of triangle, A = Area The area of △ ARC b = AR = 4 cm h = AB + BC = 4 + 2.2 = 6.2 cm A = (1/2) * 4 * 6.2 = 12.4 cm² The area of △ ARB b = AR = 4 cm h = AB = 4 cm A = (1/2)*4*4 = 8 cm² The area of △ BRC A = area of △ ARC - area of △ ARB A = 12.4 cm² - 8 cm² = 4.4 cm² Ratio of areas of △ ARB and △ BRC Ratio = △ ARB : △ BRC = △ ARB ÷ △ BRC = 8 cm² ÷ 4.4 cm² = 1.81818 The final answer is: Ratio = area △ ARB : area △ BRC = 1.81818… , or 2 : 1.1 Thanks for writing. Staff www.solving-math-problems.com