A cube has a surface area of 216 square inches. What is the edge length of the cube? Plz give a step by step answer

 6 inches

Explanation:

A cube is made up of 6 square faces. For now, focus on one square only. Let's say that square has a side length of x. So the area of that square is x*x = x^2. Since there are 6 faces, this means there is a total surface area of 6x^2

So,

SA = 6x^2

Replace the "SA" with 216 since we know the surface area. Then solve for x

216 = 6x^2

6x^2 = 216

x^2 = 216/6 divide both sides by 6

x^2 = 36

x = sqrt(36)

x = 6

If each square has a side length of x = 6 inches, then each square has an area of x^2 = 6^2 = 36 square inches. Then we multiply by 6 to get a total surface area of 6*36 = 216 square inches. This confirms the answer. You can use the formula to confirm the answer as well.

SA = 6x^2

SA = 6*6^2

SA = 6*36

SA = 216

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12