Leo wants to paint a mural that covers a wall with an area of 1734 swuate feet. The height of the eall is 2/3 of its length.What is the length and the height of the wall?
L (2 L/3) = 1734
so
2 L^2/3 = 1734
L^2 = 3*1734/2
L = sqrt (2601)
To find the length and height of the wall, we need to solve a system of equations.
Let's start by assigning variables to the unknowns:
Let L be the length of the wall.
Let H be the height of the wall.
We are given that the area of the wall is 1734 square feet: L * H = 1734 -- Equation (1)
We are also given that the height is 2/3 of the length: H = (2/3) * L -- Equation (2)
Now, we can solve this system of equations by substituting Equation (2) into Equation (1).
Substituting Equation (2) into Equation (1):
L * [(2/3) * L] = 1734
(2/3) * L^2 = 1734
Multiplying both sides by 3: 2 * L^2 = 5202
Dividing both sides by 2: L^2 = 2601
Taking the square root of both sides: L = 51 or L = -51 (ignore since the length cannot be negative)
Therefore, the length of the wall is 51 feet.
Substituting the length into Equation (2) to find the height:
H = (2/3) * 51
H = 34 feet
Therefore, the length of the wall is 51 feet and the height is 34 feet.