SOLUTION: the product of two consecutive positive even integers is twelve more than three times the smaller integers find the integers. plus the base of a triangle is 2cm less than four tim

Question 17376: the product of two consecutive positive even integers is twelve more than three times the smaller integers find the integers. plus the base of a triangle is 2cm less than four times the height. the area of thr triangle is 45 sq cm. find the height and the length of the base of the triangle.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
the product of two consecutive positive even integers is twelve more than three times the smaller integers find the integers.
let the smaller even number be 2n and next even number is 2n+2..
their product=2n(2n+2)=4n^2+4n..this is equal to ...
three times smaller integer+12=3*2n+12=6n+12..hence
4n^2+4n=6n+12
4n^2-2n-12=0
2n^2-n-6=0
2n^2-4n+3n-6=0
2n(n-2)+3(n-2)=0
(n-2)(2n+3)=0
hence n=2 is the smaller integer and 4 is the next integer....
plus the base of a triangle is 2cm less than four times the height. the area of thr triangle is 45 sq cm. find the height and the length of the base of the triangle.
area of a triangle=(1/2)*base*height
let the height be h..four times the height =4h...less 2 cm =4h-2 ..this is equal to base =b
hence b=4h-2
area=45=(1/2)(4h-2)h=(2h-1)h=2h^2-h
2h^2-h-45=0
2h^2-10h+9h-45=0
2h(h-5)+9(h-5)=0
(h-5)(2h+9)=0..
hence h=5
base 4h-2=4*5-2=18
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