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Flura [38]
1 year ago
14

A photograph is 3 in. longer than it is wide. When a 2-in. border is placed around the photograph, the total area of the photogr

aph and the border is 108 in^2. Find the dimensions of the photograph.​
Mathematics
1 answer:
Vsevolod [243]1 year ago
4 0

width = 7

length = 10

Step-by-step explanation:

solve for the one letter that gets talked about the most

which is w or width

width = w

length = 3 + w

2 inch border means

width = w + 2

length = 3 + w + 2

area = length times width

area = ( 3 + w + 2 ) times (w + 2 )

108 = ( 3 + w + 2 ) times (w + 2 )

108 = ( w + 5 ) times (w + 2 )

( w + 5 ) times (w + 2 ) = 108

w^2 + 7w +10 = 108

w^2 + 7w - 98 = 0

going to make w = x

x^2+7x-98=0

(x-7)(x+14)

x = 7

x = -14

w=7

w= -14

cant have a negative measurement so w=7 is used

width = w

length = 3 + w

width = 7

length = 3 + 7 = 10

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N the diagram, and are horizontal lines and is a vertical line segment. If FB : FC = 4 : 3, what are the coordinates of point D?
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<span>Given the diagram, where AB and EF are horizontal lines and CB is a vertical line segment. Given that FB : FC = 4 : 3, From the diagram, the coordinate of A is (-10, -8) and the coordinate of C is (-3. -1). We can also see that the coordinate of B is (-3, -8) (since CB is a vertical line means that B is the same x-value as C and AB is a horizontal line means that B is the same y-value as A) Recall that the coordinate of a point dividing a line segment in the ratio m:n is given by (x1 + m/(m+n) (x2 - x1), y1 + m/(m+n) (y2 - y1)) Thus, since FB : FC = 4 : 3, this means that point F divides the line segment BC in the ratio 4 : 3. Thus, the coordinate of F is given by (-3 + 4/(4+3) (-3 - (-3)), -8 + 4/(4+3) (-1 - (-8))) = (-3 + 4/7 (0), -8 + 4/7 (7)) = (-3, -4). Also, given that FB : FC = 4 : 3, this means that point D divides the line segment AC in the ratio 4 : 3. Thus, the coordinate of D is given by (-10 + 4/(4+3) (-3 - (-10)), -8 + 4/(4+3) (-1 - (-8))) = (-10 + 4/7 (7), -8 + 4/7 (7)) = (-6, -4). Therefore, the coordinates of point D is (-6, -4).</span>
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2/5 is the answer
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