A rectangle has a diagonal with length 8 centimeters, its length is 4 centimeters greater than the width, how do you find the length and width of the rectangle?

1 Answer
Mar 15, 2018

Answer:

The width is #3.29# cm
The length is # 7.29# cm

Explanation:

The angles of a rectangle are #90°#

A diagonal bisects the rectangle and forms two right-angled triangles.

The width is the shorter side, let it be #x# cm
The length is #4# cm longer, so it is #x+4# cm
The diagonal is the hypotenuse of the triangle and has a length of #8# cm.

Use Pythagoras' Theorem to write an equation:

#x^2 + (x+4)^2 = 8^2#

#x^2 + x^2 +8x+16 = 64#

#:. 2x^2 +8x -48 =0" "larr div 2#

#x^2 +4x -24 =0" "larr# does not fcatorise

Solve by completing the square.

#x^2 +4x color(blue)(+4) = 24 color(blue)(+4)#

#(x+2)^2 = 28#

#x = +-sqrt28-2#

#x = 3.29cm#

#x = -7.29cm" "larr# reject as a length of a side

The width is #3.29# cm
The length is #3.29+4= 7.29# cm