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Alla [95]
3 years ago
10

2. A poster is 15 cm taller than it is wide. It is mounted on a piece of cardboard so that there is a 10 cm border on all sides.

If the area of the border alone is 950 cm, what are the dimensions or the poster?​
Mathematics
1 answer:
lilavasa [31]3 years ago
4 0
Set up two equations
T = how tall
W = how wide.
T = W + 25 is the first equation
5
×
{
2
(
T
+
10
)
}
+
5
×
(
2
×
W
)
=
1350
This equation is the total height adding 5 for the top border and 5 for the bottom border. Then multiplying the total height by the width of the border 5, time 2 because there are two sides that are tall Then adding 5 times two widths.
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Find the length, width and perimeter of 3 possible different rectangles given the area of 12 square units. Fill out the table be
klemol [59]
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The base of a triangle is twelve more than twice its height. If the area of the triangle is 42 square centimeters, find its base
kolezko [41]

Hello from MrBillDoesMath!

Answer:

h =  ( -6 + sqrt(204) ) / 2

b =   6 + sqrt(204)

Discussion:

Area of a triangle = (1/2) b h

where "b" is the length of the base and "h" is the height of the altitude.

We are told that

A = (1/2) * (2h +12)* h  and

A = 42.

Equating both sides gives

(1/2) (2h+12)*h = 42.

Multiplying both terms in the left side by (1/2) gives:

(  (1/2) 2h + (1/2) 12) ) * h = 42  or

(h + 6) * h = 42 or

h^2 + 6h = 42.  Subtract 42 from both sides:

h^2 + 6h - 42 = 0.

Using the quadratic formula:


h = ( -6 + sqrt( 6^2 - 4(1)(-42) )    / 2(1) =

     ( -6 + sqrt (36+ 168) )   / 2             =

     ( -6 + sqrt(204) ) / 2

Not a nice number.


Base = 2h + 12 =  

    { ( -6 + sqrt(204) ) /2  }  * 2     + 12  =

    (-6 + sqrt(204)) + 12  =

     6 + sqrt(204)


Thank you,

MrB

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