math
posted by sheila on .
i need help in solving these 2 problems...please help..thank you...
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??

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:
(x96)(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 
x * ( x + 4 ) = 9600
x^2 + 4 x  9600 = 0
solve quadratic
area = (1/2) b h
420 = (1/2) b (5b+10)
840 = 5 b^2 + 10 b
b^2 + 2 b  168 = 0
solve quadratic