The sum of the distances from the point of intersection of the diagonals of the rectangle to the adjacent sides is 22 cm. One of the sides of the rectangle is 6 cm less than the other. Find these sides.
We drop 4 perpendiculars from the point of intersection of the diagonals of the rectangle on its sides.
In total, all 4 perpendiculars will give the sum of the two sides of the rectangle, since they will continue each other in pairs, and the sum will simply be the sum of the length and width.
Let’s introduce variables:
Let m be one side of the rectangle and n the other side.
Let’s compose and solve a system of two equations with two unknowns:
m + n = 22;
m – n = 6;
We add the equations and get:
2 * m = 28;
m = 14;
n = 8.
The sides of the rectangle are 14 cm and 8 cm.
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