GEOMETRY: Find the perimeter of the polygon if Angle B is congruent to Angle D

Given:

∠B ≅ ∠D

AB = 11.5 cm

To find:

The perimeter of the polygon.

Solution:

The reference image for the answer is attached below.

AP and AS are tangents drawn from the external point A.

BP and BQ are tangents drawn from the external point B.

CQ and CR are tangents drawn from the external point C.

DR and DQ are tangents drawn from the external point D.

If two tangents drawn from an same external point to a circle, then the lengths of tangents are equal.

⇒ AP = AS,   BP = BQ,   CQ = CR,   DR = DS

AS = 11.5 cm

BP = BQ

BP = 12.5 cm

CQ = CR

CQ = 13.5 cm

Given ∠B ≅ ∠D

⇒ DS = DR = 12.5 cm

Perimeter of polygon = AP + BP + BQ + CQ + CR + DR + DS + AS

                                    = 11.5 + 12.5 + 12.5 + 13.5 + 13.5 + 12.5 + 12.5 + 11.5

                                    = 100

The perimeter of the polygon is 100 cm.

the answer is b i just did that

step-by-step explanation:

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.