how much shorter is it to walk diagonally across a rectangular field 40m lenght and 30m breadth, than along two of its adjacent sides? please solve the question.
Answers
Answer:20m
Step-by-step explanation:
The diagonal divides the rectangular into two equal right-angled triangles.
The distance of the diagonal is calculated by adding the squares of the length and bredth,the find its squareroot
So: diagonal=√{40^2 + 30^2}
D=√[1600+900]
D=√2500
D=50m
We then add the total distance he would have covered if he travelled along the length and bredth.
40+30=70
We minus our diagonal.
70-50=20
I hope its well explained
Solution:-
Given:-
- Length = 40m
- Breadth = 30m
Let "x" be the Diagonal of the Rectangular Field.
∵ It's a Rectangular Field.
∴ The Diagonal of the Field will be the Hypotenuse.
By Pythagoras Theorem,
=) x²=30²+40²
=) x²= 900 + 1600
=) x² = 2500
=) x = √2500
=) x = 50
∴ Hypotenuse = 50m
When he walks along the two of its adjacent sides. The Distance Covered = 30 + 40 = 70m
But when he walks across the Diagonal he covers 50m Distance.
=) Distance saved by walking across Diagonal = 70m - 50m = 20m
∴ He will save 20m by walking across Diagonal.