```Question 307737
1. the dimensions of a rectangular flower garden were 8 m by 15 m. Each dimension was increased by the same amount. The garden then had an area of 198 m squared. Find the dimensions of the new garden.

the dimensions of flower garden

length = 15 m
width = 8 m
.
increase each dimension by x m
then the dimensions become
x+15
x+8
The area of the garden after increase in dimension = 198 m^2

Area = L * W

(x+15)(x+8) =198
x(x+8)+15(x+8)=198
x^2+8x+15x+120=198
x^2+23x-78=0 ....      (-198+120)
x^2+26x-3x-78=0
x(x+26)-3(x+26)=0
(x+26)(x-3)=0
x=-26 OR x=3

x=3 is practical and valid

The new length = 15 +3=18 m
The new width = 8 +3 = 11
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2.  a 7 x 10 in mirror was put in a frame and hung on the wall, the mirror and frame together cover an area of 130 in squared. How wide is the frame?

length of mirror = 10
width of mirror = 7

Let the width of the border be x
Dimensions of frame

New length = 10+2x
New width = 7+2x

(2x+7)(2x+10)=130 in squared

2x(2x+10)+7(2x+10)=130
4x^2 +20x +14x +70=130
4x^2+34x - 60 =0
2x^2+17x-30=0
2x(x+10)-3(x+10)=0
(2x-3)(x+10)=0

x=3/2 OR x= -20.. ( width of border = 3/2 . so increase in width is double)

3 inches is the increase in width

frame width = 7+3=10 inches

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