Sam has a rectangular garden ABCD of dimension 30m x 20 m. He wants to design a
flower bed F in between such that the distance of the flower bed from one corner is
exactly one half of the distance from the opposite corner. If we take the co ordinates of B
(0,0), answer the following:
4(i) Write the coordinates of (i) A (ii) C
(ii) Find the length AC.
(iii) What is the ratio in which F divides AC?
(iv) Write the coordinates of F.
Answers
Step-by-step explanation:
Given:Sam has a rectangular garden ABCD of dimension 30m x 20 m. He wants to design a
flower bed F in between such that the distance of the flower bed from one corner is exactly one half of the distance from the opposite corner. If we take the co ordinates of B (0,0).
To find:
i) Write the coordinates of (i) A (ii) C
(ii) Find the length AC.
(iii) What is the ratio in which F divides AC?
(iv) Write the coordinates of F.
Solution:
Step 1: Firstly draw point B at (0,0).
Now following the order ABCD,length as 30m and breadth as 20 m.Put all the points.As shown in attached figure. One possible way is shown.
Step 2: Write the coordinates of A and C.
Coordinates of A (0,30)
Coordinates of C (20,0)
Step 3: Length of AC
Because ∆ABC is right triangle,right angle at B.(According to property of Rectangle)
Length of AB= 30 m
Length of CB=20 m
Length of AC can be calculate using Pythagoras theorem
AC²=AB²+CB²
AC=√(900+400)
AC=√1300
AC=36.05 m
Step 4:Find ratio in which F divides AC?
ATQ,
F divides AC in 2:1
Step 5: Write the coordinates of F.
Since F divides AC in 2:1
Apply internal section formula
F(x,y)=[(2×20+1×0)/3,(2×0+1×30)/3]
F(x,y)=(40/3,30/3)
F=(13.33,10)
Hope it helps you.
Note*: Section Formula is written in explanation of Q2 below.
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