420 algebra De mystif ieD
- The width of a rectangle is three-fourths its length. The diagonal is
10 inches. What are its dimensions? - The diameter of a rectangular classroom is 34 feet. The room’s length is
14 feet longer than its width. How wide and long is the classroom?
✔SOLUTIONS
When there is more than one solution to an equation and one of them is
not valid, only the valid solution will be given.- Let x represent the length of each side (in feet). The diagonal is 60 feet,
so D = 60. The formula DL^22 = + W^2 becomes 60^2 = x^2 + x^2.
60
3600 2
3600
2
1800
1800
30 2
30222
2
222=+
=
==
=
⋅=xx
x
xx
x
x
22 =xThe length of the square’s sides is 30 2 feet, or approximately 42.4 feet.- The length is 14 cm more than the width, so L = W + 14. The diameter is
34 cm, so D = 34. The formula DL^22 = + W^2 becomes 3422 = WW+ 14 )+ ( ^2.
34 14
1156 14 14
1156 28 1222
2
2=++
=+ ++
=+ +()
()()WW
WW W
WW 996
1156 228 196
02 28 960
1
20 1
222
2
22+
=++
=+−
=W
WW
WW
() (W ++−=+ −
=− +28 960014 480
016302WWW
WW)()()
W − 16 = 0 W + 30 = 0 (This does not lead to a solution.)
W = 16
The width is 16 cm and the length is 16 + 14 = 30 cm.