Question

he horses on a ranch are kept in two pens shaped like similar rectangles. The perimeter of the larger pen is 30% greater than the perimeter of the smaller pen. If the area of the smaller pen is 1,200 square meters, what is the area of the larger pen?

Answer 1

Use ratios. If the perimeter of the larger pen is 30% greater than the perimeter of the smaller pen, then the ratio of the perimeter of the larger pen to the smaller pen is \(\Large\frac{1+30\%}{1}\)
The ratio of two similar shapes' areas is the square of the ratio of their perimeters. So...
\(\Large(\frac{1.3}{1})^2\)

And the smaller pen is 1200 square meters, so using that and the ratio above, you can find the area of the larger pen.
\(\Large(\frac{1.3}{1})^2=\frac{A_L}{1200}\)

Solve for \(A_L\)

Answer 2

okay 1.3 divided by 1 times 2 equals 2.6...... so i divide 2.6 by 1,200????

Answer 3

No...the 2 means to the power of 2, not multiply by 2.
\(\Large(\frac{1.3}{1})^2=\frac{A_L}{1200}\rightarrow\large(1.3)^2=\Large\frac{A_L}{1200}\rightarrow\large(1.3)(1.3)=\Large\frac{A_L}{1200}\)

Answer 4

OMG thanx!!! okay the answer is 2,028