Triangle XYZ is similar to triangle RST. Area of triangle XYZ is 2304 cm2 and area of triangle RST is 1296 cm2. If the longest side of the triangle XYZ measures 144 cm, then what will be the measure of the longest side of the triangle RST?
Triangle XYZ is similar to triangle RST. Area of triangle XYZ is 2304 cm2 and area of triangle RST is 1296 cm2. If the longest side of the triangle XYZ measures 144 cm, then what will be the measure of the longest side of the triangle RST? Correct Answer 108 cm
Given
Triangle XYZ is similar to triangle RST
Area of triangle XYZ is 2304 cm2 and area of triangle RST is 1296 cm2
longest side of the triangle XYZ measures 144 cm
Concept used
Ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides
Calculation
⇒ Area of triangle XYZ : Area of triangle RST = Square of side of triangle XYZ : Square of side of triangle RST
⇒ 2304 : 1296 = (144)2 : (Side of trianle RST)2
⇒ (48)2 : (36)2 = (144)2 : (Side of trianle RST)2
⇒ 48 : 36 = 144 : (Side of trianle RST)
⇒ Side of triangle RST = 36 × 3
⇒ 108 cm
