The area of an isosceles trapezoid is 45 cm2 and its height is 5 cm. Find the perimeter if one of the legs is 2/3 of the sum of the bases.

Answer:Step-by-step explanation:The formula for determining the area of a trapezoid is expressed as Area = 1/2(a + b)hWherea and b are the length of the 2 parallel sides or bases of the trapezoid. Since it is an isosceles trapezoid, then the length of the 2 legs are equal.h represents the height of the trapezoid.From the information given,Area = 45cm²h = 5 cm45 = 1/2(a + b)52 × 45 = 5(a + b)90 = 5(a + b)a + b = 90/5 = 18if one of the legs is 2/3 of the sum of the bases, it means that the height of each leg is 2/3 × 18 = 12 cmThe length of both legs is 12 × 2 = 24 cmThe perimeter of the trapezoid is Sum of bases + sum of legsTherefore,Perimeter = 18 + 24 = 42 cm