Question

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a builder makes all of their ramps with a base to height ratio of 12 : 1 to be wheelchair - accessible. see the diagram below, which is not drawn to scale:
diagram showing base 12 and height 1
a certain ramp needs to cover a height of 0.8 meters.
diagram showing ramp length ℓ and height 0.8 m
what is the length ℓ of this ramp?
round your answer to the nearest hundredth of a meter.
answer box m
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Explanation:

Step1: Find the base length

The base to height ratio is \( 12:1 \). Let the base be \( b \) and height be \( h = 0.8 \) meters. From the ratio \( \frac{b}{h}=\frac{12}{1} \), so \( b = 12\times h \). Substituting \( h = 0.8 \), we get \( b = 12\times0.8 = 9.6 \) meters.

Step2: Use Pythagorean theorem to find ramp length

The ramp, base, and height form a right triangle. By Pythagorean theorem, \( \ell=\sqrt{b^{2}+h^{2}} \). Substituting \( b = 9.6 \) and \( h = 0.8 \), we have \( \ell=\sqrt{9.6^{2}+0.8^{2}}=\sqrt{92.16 + 0.64}=\sqrt{92.8}\approx9.63 \) meters.

Answer:

\( 9.63 \)