In a triangle ABC ., X and Y are the mid points of sides AC and CB respectively .
If area of the triangle XCY is 47
2
cm2
then find the sum of area of the triangles
ABC and XCY .
Answers
Given : ΔABC , X Y are the mid points of side AC & CB respectively
area of the ΔXCY is 47 cm²
To Find : sum of area of the triangles ΔABC and ΔXCY
Solution:
line joining the mid-point of two sides of a triangle is equal to half the length of the third side and parallel to third side
Hence XY = AB/2 => AB/XY = 2
XY || AB
=> ∠X = ∠A , ∠Y = ∠B ( corresponding angles)
∠C is common
=> ΔABC ≈ ΔXCY
Ratio of area of similar triangle = ( ratio of corresponding sides)²
=> ar ΔABC / ar ΔXCY = ( 2)²
=> ar ΔABC /47 = 4
=> ar ΔABC = 188 cm²
sum of area of the triangles ΔABC and ΔXCY = 188 + 47
= 235 cm²
sum of area of the triangles ΔABC and ΔXCY = 235 cm²
Learn More
Triangle ABC is formed by joining the midpoints of sides of triangle ...
https://brainly.in/question/30863565
If P (-1,1) is the midpoint of the line segment joining A(-3,b) and B (1 ...
brainly.in/question/13203314
In a triangle ABD, C is the midpoint of BD. If AB=10, AD=12, AC=9 ...
brainly.in/question/13399658