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Which roof is steeper: one with a rise of 8 and run of 4, or one with a rise of 12 and a run of 7?

1 Answer

Nov 8, 2016

The first roof is steeper.

Explanation:

Let's write the slopes as fractions first:

$S l o p e = m = \frac{rise}{run}$ $Slope = m ="rise"/"run"$

$m_{1} = \frac{8}{4} and m_{2} = \frac{12}{7}$ $m_1 = 8/4 and m_2 = 12/7$

To compare them:

as simplified fractions. $m_{1} = 2 and m_{2} = 1 \frac{5}{12}$ $m_1 = 2 and m_2 = 1 5/12$
as fractions with a common denominator:

$m_{1} = \frac{56}{28} and m_{2} = \frac{48}{28}$ $m_1 = 56/28 and m_2 = 48/28$

as decimals:

$m_{1} = 2 and m_{2} = 1.716$ $m_1 = 2and m_2 = 1.716$

In all cases we see that the first roof is steeper.

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