The area of the parallelogram is 45 cm2, and its perimeter is 40 cm. The height drawn to one of its sides is 5 times

The area of the parallelogram is 45 cm2, and its perimeter is 40 cm. The height drawn to one of its sides is 5 times less than this side. Calculate: given height; the side to which it is drawn; the second side of the parallelogram.

Given:
ABCE – parallelogram,
S ABCE = 45 square centimeters,
R ABCE = 40 centimeters,
VN – height,
AE = 5 * VN.
Find the lengths of the sides of the parallelogram ABCE: AB, CE, BC, AE and the height BH -?
Decision:
1. Consider the parallelogram ABCE.
S ABCE = BH * AE;
45 = VN * 5 * VN;
45 = 5 * BH ^ 2;
BH ^ 2 = 45: 5;
BH ^ 2 = 9;
BH = 3.
2.AE = 5 * 3 = 15.
3. Opposing sides are equal to each other in a parallelogram, then BC = AE = 15, AB = CE.
P avce = AB + CE + BC + AE;
40 = AB + AB + 15 + 15;
40 = 2 * AB + 30;
2 * AB = 40 – 30;
2 * AB = 10;
AB = 10: 2;
AB = 5.
Answer: BH = 3, BC = AE = 15, AB = CE = 5.