Question

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 1

Answer:

Step-by-step explanation:

The formula for determining the area of a trapezoid is expressed as

Area = 1/2(a + b)h

Where

a 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 = 45cm²

h = 5 cm

45 = 1/2(a + b)5

2 × 45 = 5(a + b)

90 = 5(a + b)

a + b = 90/5 = 18

if 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 cm

The length of both legs is

12 × 2 = 24 cm

The perimeter of the trapezoid is

Sum of bases + sum of legs

Therefore,

Perimeter = 18 + 24 = 42 cm