The area of a rectangle is 50 square millimeters. The width is one-half the length. Find both the length and width.

Question

 HInt L times 1/2  = 1/2L squared

Answer 1

Area of rectangle is length times width:

A=L(W)

50=L(W)

 

The width is 1/2 the length:
W=L/2

 

Substitute. Replace the W in the first equation with L/2:

50=L(W)

50=L(L/2)

50=L²/2

100=L²

10=L

 

Plug in 10 for L in either equation to solve for W:

W=L/2

W=10/2

W=5

 

The length is 10mm, and the width is 5mm.