Answer:
Step-by-step explanation:
1)
a. m∠B = m∠A
x + 25 = 2x +15
25 - 15 = 2x - x
x = 10
m∠A = 2(10) + 15 = 20 +15 = 35°
b. BE = DA
6y +6 = 2y +26
6y - 2y = 26 - 6
4y = 20
y = 20/4 = 5
BE = 6y + 6 = 6(5) + 6 = 30 +6
BE = 36
c. x = be the side of a rectangle
2x - 5 = be the other side of the rectangle
P = 2 ( l + w )
56 = 2 [ (x) + (2x - 5)]
56 = 2 (3x - 5) = 6x - 10
6x = 56 +10 = 66
x = 66/6 = 11
1 side is = 11cm
other side:
2x - 5 = 2(11) -5 = 22 -5 = 17 cm
2)
a. ME = 2 (MI)
P = 2(ME + MI)
1st solution:
P = 2 [ ME + (1/2)(ME)]
21 = 2 ME + ME = 3 ME
ME = 21 / 3 = 7 cm
2nd solution:
P = 2 [ 2(MI) + MI]
21 = 2[3MI]
21 = 6 MI
MI = 21/6 = 7/2
since: ME= 2MI = 2 ( 7/2 ) = 7cm
b. A = 44 ft²
IE = x - 1
MK = x + 2
A = (d₁)(d₂)
44 = (IE)(MK)
2(44) = 2[ (IE)(MK)]
88 = (IE)(MK) = (x-1)(x+2)
88 = x² +x -2
x² + x - 2 - 88 = 0
x² + x - 90 = 0
(x - 9 )(x + 10) = 0
x = 9 ; x = -10
x= 9 :
IE = x -1 = 9 -1 = 8
MK = x +2 = 9 +2 = 11
A = (1/2) (IE)(MK)
44 = (1/2) (8)(11) = (1/2)(88)
44 = 44
x = -10:
IE = x -1 = -10 - 1 = -11
MK= x +2 = -10 + 2 = -8
44 = (1/2)(-11)(-8) = (1/2)(88)
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Answers & Comments
Answer:
Step-by-step explanation:
1)
a. m∠B = m∠A
x + 25 = 2x +15
25 - 15 = 2x - x
x = 10
m∠A = 2(10) + 15 = 20 +15 = 35°
b. BE = DA
6y +6 = 2y +26
6y - 2y = 26 - 6
4y = 20
y = 20/4 = 5
BE = 6y + 6 = 6(5) + 6 = 30 +6
BE = 36
c. x = be the side of a rectangle
2x - 5 = be the other side of the rectangle
P = 2 ( l + w )
56 = 2 [ (x) + (2x - 5)]
56 = 2 (3x - 5) = 6x - 10
6x = 56 +10 = 66
x = 66/6 = 11
1 side is = 11cm
other side:
2x - 5 = 2(11) -5 = 22 -5 = 17 cm
2)
a. ME = 2 (MI)
P = 2(ME + MI)
1st solution:
P = 2 [ ME + (1/2)(ME)]
21 = 2 ME + ME = 3 ME
ME = 21 / 3 = 7 cm
2nd solution:
P = 2 [ 2(MI) + MI]
21 = 2[3MI]
21 = 6 MI
MI = 21/6 = 7/2
since: ME= 2MI = 2 ( 7/2 ) = 7cm
b. A = 44 ft²
IE = x - 1
MK = x + 2
A =
(d₁)(d₂)
44 =
(IE)(MK)
2(44) = 2[
(IE)(MK)]
88 = (IE)(MK) = (x-1)(x+2)
88 = x² +x -2
x² + x - 2 - 88 = 0
x² + x - 90 = 0
(x - 9 )(x + 10) = 0
x = 9 ; x = -10
x= 9 :
IE = x -1 = 9 -1 = 8
MK = x +2 = 9 +2 = 11
A = (1/2) (IE)(MK)
44 = (1/2) (8)(11) = (1/2)(88)
44 = 44
x = -10:
IE = x -1 = -10 - 1 = -11
MK= x +2 = -10 + 2 = -8
A = (1/2) (IE)(MK)
44 = (1/2)(-11)(-8) = (1/2)(88)
44 = 44