Question

The parallelograms pictured are similar figures. If the perimeter of the smaller parallelogram is 22 cm, find the perimeter of the larger parallelogram.

Answer 1

Answer:

The parallelograms pictured are similar figures. If the perimeter of the smaller parallelogram is 22 cm, then perimeter of the larger parallelogram = 44 cm

Step-by-step explanation:

Area of a parallelo gram = side 1  * Sise 2  * Sin(angle between them)

Let say side of smaller parallelogram = a & b cm

Angle = between sides = x°

a + b = 22/2 = 11cm

Area of Smaller parallelogram = abSinx° = 10 cm²  - eq 1

Let say large parallelogram has side  = c & d cm

As Both parallelogram are similar

c  = ak    & d = bk    angle = x     ( k is ratio of sides)

Area of Larger parallelogram = cdSinx° = 40 cm²

ak bk Sinx° = 40  cm²

=> k² (abSinx°) = 40  cm²

=> k² 10 = 40  ( putting value of abSinx° from eq 1)

=> k² = 4

=> k = 2

c + d = ak + bk = k (a +b) = 2(a + b) = 2 * 11 = 22 cm

Perimeter of larger parallel gram = 2 * (c +d) = 2 * 22 = 44cm