Answer:
10 m by 5 m.
Explanation:
The perimeter of the rectangle is 2*7 + 2*8 = 30 m
Let the length of the grey rectangle be x and the width y then:
2x + 2y = 30
Also we are given:
xy = 50 so:
x = 50 /y
Substituting in the first equation:
2y + 2 * (50/y) = 30
2y + 100/y = 30 Multiplying through by y:
2y^2 + 100 = 30y
2y^2 - 30y + 100 = 0
y^2 - 15y + 50 = 0
(y - 5)(y - 10) = 0
y = 5, 10
Therefore x = 50 / y = 10, 5
We took x as the length so x = 10 and y = 5.