# Thread: geometry and indices/log problem

1. ## geometry and indices/log problem

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

2.
Given that $\displaystyle y=18+ax^b$ , 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 ($\displaystyle 1+2\sqrt{7}$) $\displaystyle units^2$ has length PQ ($\displaystyle 3+\sqrt{7}$) units. Given that the distance between the two parallel sides, SR and PQ is ($\displaystyle a+b\sqrt{c}$) units where a, b and c are integers. Find, without using a calculator, the values of a, b and c.

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

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

2. just solve the system:

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