In ABC if BC is one inch longer than AB, AC is 10 inches shorter than the sum of BC and AB , and the perimeter of ABC is 72 inches, find the length of BC
2007-08-10 15:47:25 · 13 answers · asked by Mosh 1 in Science & Mathematics ➔ Mathematics
P = 72in
P = AB + BC + AC
72 = AB + BC + AC
72 = AB + ((AB) + 1) + ((AB+BC) - 10)
72 = AB + ((AB) + 1) + ((AB+(AB+1)) - 10)
72 = 4AB - 8
80 = 4AB
AB = 20 in
BC = AB + 1
BC = 20 + 1 = 21 in
AC = AB + BC - 10
AC = 20 + 21 - 10 = 31 in
2007-08-10 15:55:32 · answer #1 · answered by Reese 4 · 0⤊ 0⤋
Let AB be L inches.
Therefore BC is 1 inch longer than AB so BC = ( L+1) inches.
and AC = L + (L +1) – 10 = (2 L – 9)
Perimeter = AB + AC + BC = 72 inches.
therefore L + (L + 1) + (2 L – 9) = 72
4 L – 8 = 72
4 L = 72 + 8 = 80
L= 20, BC= 20 + 1 = 21 inches.
2007-08-10 23:53:24 · answer #2 · answered by Pranil 7 · 0⤊ 0⤋
Perimeter = AB + AC + BC = 72
let us assume,
AB = L
so, BC = L+1 [as BC=AB+1]
so, AC = 2L - 9 [as AC=AB+BC-10]
so, L+L+1+2L-9=72
so,4L-8=72
so,4L=80
so,L=20 i.e. AB=20 inch
so, BC=AB+1=20+1= 21 inch [ans]
2007-08-11 01:16:10 · answer #3 · answered by sharbadeb 2 · 0⤊ 0⤋
It is soooo simple:
AB + BC + CA = 72 in.
AB + AB + 1 + BC + AB - 10 = 72 in.
3AB + AB + 1 - 9 = 72 in.
4AB = 72 + 8 = 80
AB = 20
BC = 21
CA = 31
2007-08-10 15:55:32 · answer #4 · answered by Hell's Angel 3 · 0⤊ 0⤋
Perimeter = AB + AC + BC = 72
AB = L
BC = L+1
AC = 2L - 9
Looks like L= 20 and BC=21
2007-08-10 15:52:46 · answer #5 · answered by cattbarf 7 · 0⤊ 0⤋
Given:
1) AB + 1 = BC
2) AB + BC = AC + 10
3) AB + BC + AC = 72
Hence:
From (1):
AB + 1 = BC
AB = BC -1
Replace AB = BC - 1 into (2) and (3).
From (2):
AB + BC = AC + 10
BC - 1 + BC = AC + 10
2BC = AC + 11 .......... Equation (4)
From (3):
AB + BC + AC = 72
BC - 1 + BC + AC = 72
2BC + AC = 73
2BC = 73 - AC .......... Equation (5)
Sum up both side of equations 4 and 5.
2BC + 2BC = AC + 11 + 73 - AC
4BC = 84
BC = 84/4
BC = 21
2007-08-10 15:57:45 · answer #6 · answered by wow 2 · 0⤊ 0⤋
enable AB be L inches. consequently BC is a million inch longer than AB so BC = ( L+a million) inches. and AC = L + (L +a million) – 10 = (2 L – 9) Perimeter = AB + AC + BC = seventy two inches. consequently L + (L + a million) + (2 L – 9) = seventy two 4 L – 8 = seventy two 4 L = seventy two + 8 = 80 L= 20, BC= 20 + a million = 21 inches.
2017-01-04 04:57:28 · answer #7 · answered by Anonymous · 0⤊ 0⤋
bc = ab + 1
ac = (bc + ab) - 10
ab + bc + ac = 72
ab + (ab + 1) + ((ab+1)+ab - 10) = 72
4ab - 8 = 72
ab = 20
bc = 20 + 1 = 21
2007-08-10 16:14:38 · answer #8 · answered by querier 2 · 0⤊ 0⤋
BC=AB+1,AC=BC+AB-10
AB+BC+CA=72
AC=72-AC-10
2AC=62
AC=31
AB+AB+1+31=72
2AB=40
AB=20
BC=20+1=21 ''ANS
2007-08-10 16:00:38 · answer #9 · answered by Anonymous · 0⤊ 0⤋
BC=AB-1
AC=(BC+AB)+10
AB+BC+CA=72
(BC+1)+BC+(BC+BC+1)+10=72
4BC=72-12
BC=60/4
BC=15
2007-08-10 16:15:44 · answer #10 · answered by Bryan 1 · 0⤊ 0⤋