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