In rectangle MNPQ with side MN = 16 in, point L is the midpoint of PQ and m∠QLM = 45°. Find the perimeter of the rectangle.

Question

 What is the perimeter?

Answer 1

48

 

Sketch the rectangle.

MN and PQ are opposite sides of the rectangle so PQ's length is also 16.

L is the midpoint of PQ so LQ is 8.

The 45° angle QLM forms an isosceles right triangle so leg MQ = LQ = 8.

That's the other dimension of the rectangle.

The perimeter is 2(16 + 8) = 48.