The perimeter of a rectangular is 58 cm. the length is 5 more than twice the width. set up an expression for the length using w for width. set up an equation to find the perimeter. solve the equation to find the values of the length and the width (show your work)

a) l = 5 + 2w

b) P = 2(l +w) = 2(5 +2w +w)

c) w = 8 cm, l = 21 cm

Explanation:

a) Using w for width, twice the width is 2w, and 5 more than that is 5+2w. This is your expression for l:

... l = 5 + 2w

b) The perimeter is the sum of the lengths of all sides, so is the sum of twice the length and twice the width.

... P = 2(l +w) = 2(5 +2w + w) . . . . substituting for l using the expression of (a)

c) Substituting the given perimeter, we have ...

... 58 = 2(5 +3w) = 10 + 6w . . . . . collect terms, eliminate parentheses

... 48 = 6w . . . . . . . . . . . . . . . . . . subtract 10

... 8 = w . . . . . . . . divide by 6

... l = 5 + 2·8 = 21 . . . . . find length using the formula for it

Dimensions are in centimeters, so we can write the solution as ...

width = 8 cmlength = 21 cm

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