Find the perimeter of the polygon if B = D

Perimeter of the polygon is 92 cm

Solution:

The reference image for the solution is attached below.

AX = 10.5 cm, BY = 11.5 cm and CZ = 12.5 cm

AW and AX are tangents to the circle from external point A.

BX and BY are tangents to the circle from external point B.

CY and CZ are tangents to the circle from external point C.

DZ and DW are tangents to the circle from external point D.

Two tangents drawn from an external point to a circle are equal in length.

AW = AX, BX = BY, CY = CZ and DZ = DW

⇒ AW = AX

AW = 10.5 cm

⇒ BX = BY

BX = 11.5 cm

⇒ CY = CZ

CY = 12.5 cm

Given ∠B ≅ ∠D

If two angles are congruent, then the corresponding sides are congruent.

BX = BY = DZ = DW

DZ = DW = 11.5 CM

Perimeter = AW + AX + BX + BY + CY + CZ + DZ + DW

                = 10.5 + 10.5 + 11.5 + 11.5 + 12.5 + 12.5 + 11.5 + 11.5

                = 92

Perimeter of the polygon is 92 cm.

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step-by-step explanation:

correct answers below: