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A rectangular playground is 24 meters wide and has the same area as another rectangular playground that is 64 meters long and 48 meters wide. What is the perimeter of the first playground?
Area of the second playground: $64 \times 48 = 3072$ square meters.
The first playground has width 24 m and the same area:
$24 \times \text{length} = 3072$
$\text{length} = \dfrac{3072}{24} = 128$ meters.
Perimeter $= 2(24 + 128) = 2 \times 152 = \mathbf{304}$ meters.
$\log(x/m) = \log k + (1/n)\log P$.
Comparing this to the straight-line equation $y = mx + c$:
- $y = \log(x/m)$
- $x = \log P$
- Slope ($m$) = $1/n$
- Intercept ($c$) = $\log k$
The volume of a cube is 64.
Compare:
Column A: The area of the base of the cube
Column B: $32$
For a cube with volume $V = s^3 = 64$, the side length is $s = \sqrt[3]{64} = 4$.
The base of a cube is a square, so its area $= s^2 = 4^2 = 16$.
Column A = 16, Column B = 32.
Since $16 < 32$, Column B is greater.
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