CASE STUDY QUESTION 50-Class X-Maths
CASE STUDY QUESTION 50-Class X-Maths
In one of the residential colony of city, there is a triangular park ABC available. The Resident Welfare Association of the colony wishes to divide this park into two parts of equal areas. One for planting trees and raising a lawn and the other for providing place for children park for playing activities. One of the members Ram suggested to draw a line segment XY || BC for the same.
(i) Which is the correct similarity criteria is used for above triangles ABC and XBY?
(a) SSS (b) AAA (c) RHS (d) ASA
Ans: (b) AAA
(ii) What is the ratio of areas of ∆ABC : ∆ XBY?
(a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 1 : √2
(iii) If ∠BXY = 60°, then ∠BAC is :
(a) 80° (b) 60° (c) 140° (d) 100°
∠BXY = ∠BAC (Corresponding angles)
⸫ ∠BAC = 60°
(iv) If the ratio of areas of ∆BXY : ∆ ABC is 1 : 2, then XB : AB is :
(a) 1 : 2 (b) 1 : 4 (c) 2 : 4 (d) 1 : √2
(v) If the area of ∆ AXY is 128 m2, then what will be area of ∆ CXY.
(a) 128 m2
(b) 248 m2
(c) 256 m2
(d) 48 m2
∆ AXY and ∆ CXY are lie on the same base XY and between the same parallels AC || XY.
⸫ ar(∆ AXY) = ar(∆ CXY)
⸫ ar(∆ CXY) = 128 m2
