The smaller base of the BC of the ABCD trapezoid is 7cm. A straight line is drawn through vertex B, parallel to the side CD.
| February 22, 2021 | education
The smaller base of the BC of the ABCD trapezoid is 7cm. A straight line is drawn through vertex B, parallel to the side CD. The perimeter of the triangle cut off from the trapezoid is 16cm. Find the perimeter of the trapezoid.
In the BCDH quadrangle, the HВ side is parallel to the CD by the condition, the BC side is parallel to the DH by construction, then the BCDH is a parallelogram, and therefore DH = BC = 7 cm, BH = CD.
The perimeter of the triangle is Equ = AB + AH + BH = AB + AH + CD = 16 cm.
Base length AD = AH + AD.
The perimeter of the trapezoid is: Ravsd = AB + BC + CD + AD = (AB + AH + CD) + DH + BC = 16 + 7 + 4 = 30 cm.
Answer: The perimeter of the trapezoid is 30 cm.
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