# Thread: [SOLVED] SAT math page 656

1. ## [SOLVED] SAT math page 656

In the figure below, PQRS is a rectangle, and points Q and R lie on the graph of y=ax^2, where a is a constant. If the perimeter of PQRS is 10, what is the value of a?

From the graph I got that the length of the rectangle is 3 and the width is 2. Is this correct? I don't know what to do next. Thanks in advance

2. Originally Posted by fabxx
In the figure below, PQRS is a rectangle, and points Q and R lie on the graph of y=ax^2, where a is a constant. If the perimeter of PQRS is 10, what is the value of a?

From the graph I got that the length of the rectangle is 3 and the width is 2. Is this correct? I don't know what to do next. Thanks in advance
You know that the distance PQ is 3.
The coordinates of P are (-1;0). Since PQ is parallel to the y axis, their x-ordinate are the same : -1.
And the distance PQ will be the difference between their y-ordinates.
So point Q has coordinates (-1;3)

Now, substitute them into y=ax˛ to get a.

3. is it like this?

Because y=3 and x=(-1)
and because y=ax^2
so therefore 3=a(-1)^2
so a=3?

Thanks in advance

4. Originally Posted by fabxx
is it like this?

Because y=3 and x=(-1)
and because y=ax^2
so therefore 3=a(-1)^2
so a=3?

Thanks in advance
Yes it is

5. Thanks Moo! You're very helpful!