# Thread: geometry and indices/log problem

1. ## geometry and indices/log problem

1.
A parallelogram PQRS with area ( $1+2\sqrt{7}$) $units^2$ has length PQ ( $3+\sqrt{7}$) units. Given that the distance between the two parallel sides, SR and PQ is ( $a+b\sqrt{c}$) units where a, b and c are integers. Find, without using a calculator, the values of a, b and c.

2.
Given that $y=18+ax^b$ , y=56 when x=4 and y=20 when x=2.5, find the value of a and b.

2. Originally Posted by wintersoltice
1.
A parallelogram PQRS with area ( $1+2\sqrt{7}$) $units^2$ has length PQ ( $3+\sqrt{7}$) units. Given that the distance between the two parallel sides, SR and PQ is ( $a+b\sqrt{c}$) units where a, b and c are integers. Find, without using a calculator, the values of a, b and c.

2.
Given that $y=18+ax^b$ , y=56 when x=4 and y=20 when x=2.5, find the value of a and b.
1.
$A_{\mbox{parallelogram}} = Bh$

where $B= 3+\sqrt{7}$, $h=a+b\sqrt{c}$ and $A = 1+2\sqrt{7}$

2. just solve the system:

56 = 18 + a(4)^b
20 = 18 + a(2.5)^b