One of the diagonals of the rhombus is 4 times smaller than the other, and its area is 242.

One of the diagonals of the rhombus is 4 times smaller than the other, and its area is 242. Find the large diagonal of the rhombus.

1. The vertices of the rhombus A, B, C, D. О – the point of intersection of the diagonals.

2. The AC diagonal divides the rhombus into two triangles. The area of each of them is equal to 1/2 of the area of the rhombus = 242: 2 = 121 units of measurement².

3. АС = 4 ВD.

4. OD = 1/2 ВD.

3. Area of the triangle ACD = AC x OD / 2 = 121 measurement units². We substitute here 1/2 ВD instead of OD and 4 ВD instead of АС:

4 ВD x ВD / 4 = 121 measurement units².

ВD – 11 units.

AC = 11 x 4 = 44 units.

Answer: large AC diagonal = 44 units.