# math

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Your home is built on a square lot. To add more space to your yard, you purchase an additional 4 feet along the side of the property. The area of the lot is now 9600 square feet. What are the dimentions of the new lot??

The Garys have a triangular pennant of area 420in.^2 flying from the flagpole in their yard. The height of the triangle is 10 in. than 5 times the base of the triangle. What are the dimensions of the pennant??

• math -

For the first problem:
x=length of side before the addition
x+4=the length of the longer side after the the additional 4 feet is purchased.

The new area of the property is:
x(x+4)=9600
x^2 + 4x =9600
x^2 + 4x - 9600=0
which is:
(x-96)(x+100)=0
Ignore the negative solution for x since a negative number would not make much sense for a lot length.
x=96 and x+4=100

• math -

x * ( x + 4 ) = 9600

x^2 + 4 x - 9600 = 0

area = (1/2) b h
420 = (1/2) b (5b+10)
840 = 5 b^2 + 10 b

b^2 + 2 b - 168 = 0

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