7. A rectangular field, 70 m long and 50 m wide, has a path of uniform width around it. If the area of the path is 1 024 m? find the width of the path.
Answers
Answer:
Given:-
a rectangular field 70m long and 50m wide has a path of uniform width around it, the area of the path is 1024 sq.m.
To Find:-
find the width of the path
Solution:-
Draw the picture of a rectangle inside a rectangle.
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The area of the inner rectangle is 70*50 = 3500 sq.m
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Area of the outer rectangle = (70+2x)(50+2x) = 4X^2 + 240x + 3500
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Equation:
Outer area - Inner area = 4x^2+ 240x = 1024
x²+60x-256 = 0
(x-4)(x+64) = 0
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Positive Solution:
x = 4m
THEREFORE, THE WIDTH OF THE PATH = 4m
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Answer:
4 meters
Step-by-step explanation:
Draw the picture of a rectangle inside a rectangle.
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The area of the inner rectangle is 70*50 = 3500 sq. meters
---
Area of the outer rectangle = (70+2x)(50+2x) = 4X^2 + 240x + 3500
----
Equation:
Outer area - Inner area = 4x^2+ 240x = 1024
x^2+60x-256 = 0
(x-4)(x+64) = 0
---
Positive Solution:
x = 4 meters.