Select three ratios that are equivalent to 8 : 5
2 answers:
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Given:
Length of the ladder = 9.85 m
The height to the top of the ladder is 5 m more than the distance between the wall and the foot of the ladder.
To find:
The height to the top and the distance between the wall and the foot of the ladder.
Solution:
let x be the distance between the wall and the foot of the ladder. Then the height to the top of the ladder is (x+5).
Pythagoras theorem: In a right angle triangle,
In the given situation, hypotenuse is the length of ladder, i.e., 9.85 m. The base is x m and the height is (x+5) m.
Using the Pythagoras theorem, we get
Here, . Using the quadratic formula, we get
Approximating the value, we get
Distance cannot be negative so
Now we have
Therefore, the base is 4 m and the height is 9 m.
The answer is the option d, which is: d)
The explanation for this problem is shown below:
1. Smplify the denominator and rewrite the numerator in this form:
2. Multiply the denominator and the numerator by the conjugated and simplify the expression, as following:
3. As you can see, you obtain the expression shown in the option mentioned above.