1.a rectangle`s length is 5cm less than twice its width. if the length is decreased by 5 cm and width is increased by 2 cm; the perimeter of the resulting rectangle will be 74cm. find the length and the width of the original rectangle.
ans:25 and 15cm
2. a man is 42 years old and his son is 12 years old. in how many years will the age of the son be half the age of the man at that time.
ans:18 years
2006-10-21 18:18:14 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The original width is w and the original length is 2w - 5.
The next part gives you your equation:
2(2w-5-5 )+2( w + 2 ) = 74
4w - 10 - 10 + 2w + 4 = 74
6w -16 = 74
6w = 90
w = 15
2w - 5 = 25
2. The number of years we want is x. "In how many years" means we're looking at the future.
12 + x = 1/2(42 + x)
12 + x = 21 + 1/2 x
1/2 x = 9
x = 18
2006-10-21 18:33:22 · answer #1 · answered by PatsyBee 4 · 0⤊ 0⤋
1. Let L and W be the length and width.
From the given info, L = 2W - 5.
Also, 2(L-5) + 2(W+2) = 74, since the perimeter is twice the length plus twice the width.
Substitute 2W-5 for L in the second equation. You get
2(2W-5-5) + 2(W+2) = 74.
Multiply everything out:
4W-20+2W+4=74
Combine like terms:
6W=90
Solve for W:
W=15. Then L=2W-5=2(15)-5=30-5=25.
2. Let x be the number of years until the son will be half as old as the man. Then 42+x = 2(12+x).
Multiply out:
42+x = 24+2x
Rearrange:
42-24 = 2x-x
Combine like terms:
18 = x.
2006-10-22 01:25:20 · answer #2 · answered by James L 5 · 0⤊ 0⤋
1) L=length; W=width, P=perimeter
L=2W-5
If L-5 and W+2, then P=74
Problem would be: 2[(L-5) + (W+2)]=74
Substitude: 2[(2W-5-5) +(W+2)]=74
And Solve and plug in what you got for W in the original equation (L=2W-5) to find L.
2. Man= 42, Son=12, x=number of years it'll take
12+x=0.5(42+x)
Solve. 12+x=21+0.5x
0.5x=9, X=18
2006-10-22 01:34:10 · answer #3 · answered by =] 2 · 0⤊ 0⤋
ok the first problem is easy...
since the perimeter is decreased by 5 and increased by 2, that means the original perimeter is 80, because you add 10 and subtract 4 from 74, the result is 80
with this information you now have the sides of the rectangle...
2x - 5 + 2x -5 + x + x = 80
= 6x-10 = 80
= 6x = 90
x = 15
2x - 5 = 25
--------------------------------------------------------------------------------
12+x=0.5(42+x)
Solve. 12+x=21+0.5x
0.5x=9, X=18
2006-10-22 01:38:49 · answer #4 · answered by Anonymous · 0⤊ 0⤋
#2:
42-12=30 man's age at time of son's birth
30 x 2=60 son's age at time of man's age doubled
30-12=18
42+18=60
2006-10-22 01:37:18 · answer #5 · answered by Anonymous · 0⤊ 0⤋
Yup!
2006-10-22 01:28:03 · answer #6 · answered by econofix 4 · 0⤊ 0⤋