The two lines y = x and x = -5 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z? Answers
A) 16  B) 5/√2  C) 8  D) 2√2  E) (√2)/3
800score Official Solution:   The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-5, -5) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(4 × 4) = 25/2; so z = 25/2.   The next step requires us to find the length of a side of a cube that has a face area equal to 25/2. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 25/2. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 25/2. Clearly s = √25/2 = 5/√2 , oranswer choice (5/√2).
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The two lines y = x and x = -5 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?