Aroped off area of width x is created around a 4-foot by 6-foot rectangular museum of display of native american artifacts. the combined area of the display and the roped-off is 120 square feet. find the width.

Let
x----------> width a roped off area

we know that
(4+2x)*(6+2x)=120
then
4*6+4*2x+2x*6+2x*2x=120 ---> 24+8x+12x+4x²=120 -------> 4x²+20x+24=120
4x²+20x-96=0

using a graph tool---------> to calculate the quadratic equation
see the attached figure

the solution is 
x=3 ft

the answer is
the width a roped off area is 3 ft

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

Ibelieve the answer would be 7, 13, 23