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Ratio of Similar Triangles

by Ghazala
(Karachi, Pakitstan)

Similar Triangles - Ratio of Areas

Similar Triangles - Ratio of Areas








































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

Comments for Ratio of Similar Triangles

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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



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