Answer:

You can the vertical wall is built to a certain height.

we'll call it x until we can find out what the value of x is.

you are given that the width of the court is equal to 5 meters less than 6 times the height of the wall.

the width of the court is therefore equal to 6x - 5.

you are given that the length of the court is equal to 2 meters less than 8 times the height of the wall.

the length of the court is therefore equal to 8x - 2.

the floor area of the court is equal to the length of the court times the width of the court.

since the length of the court is equal to 8x - 2 and the width is equal to 6x - 5, then the area of the the court is equal to (8x - 2) * (6x - 5).

this is equal to 48x^2 - 40x - 12x + 10

combine like terms to get the area of the court is equal to 48x^2 - 52x + 10.

the area of the wall on the length side of the court is equal to x * (8x - 2) = 8x^2 - 2x.

the area of the wall on the width side of the court is equal to x * (6x - 5) = 6x^2 - 5x.

the total area of the inside face of the wall is equal to 2 * (8x^2 - 2x) + 2 * (6x^2 - 5x) = 16x^2 - 4x + 12x^2 - 10x = 28x^2 - 14x.

you are given that the area of the court is 178 meters greater than the area of the inside face of the wall.

this means that 48x^2 - 52x + 10 = 28x^2 - 14x + 178.

subtract the right side of this equation from both sides of this equation to get:

48x^2 - 52x + 10 - 28x^2 + 14x - 178 = 0

combine like terms to get:

20x^2 - 28x - 168 = 0

factor this quadratic equation to get:

x = -2.1 or x = 4.

x can't be negative, so x = 4.

that's the height of the wall.

the area of the inside face of the wall is 28x^2 - 14x = 392 square feet when x = 4.

the area of the court is 48x^2 - 52x + 10 = 570 square feet when x = 4.

570 - 392 = 178.

the area of the court is 178 meters less than the area of the inside fact of he walls, as was given