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The parallel sides AB, PQ, and CD, gives similar triangles, ∆ABD ~ ∆PQD and ∆CDB ~ ∆PQB, from which we have;
![\frac{1}{x} + \frac{1}{y}= \frac{1}{z}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7Bx%7D%20%20%2B%20%20%5Cfrac%7B1%7D%7By%7D%3D%20%20%20%5Cfrac%7B1%7D%7Bz%7D)
<h3>Which method can be used to prove the given relation?</h3>
From the given information, we have;
According to the ratio of corresponding sides of similar triangles, we have;
![\frac{x}{z} = \mathbf{\frac{BD}{QD} }](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7Bz%7D%20%20%3D%20%20%5Cmathbf%7B%5Cfrac%7BBD%7D%7BQD%7D%20%7D)
![\frac{y}{z} = \frac{BD}{ BQ}](https://tex.z-dn.net/?f=%20%5Cfrac%7By%7D%7Bz%7D%20%20%3D%20%20%5Cfrac%7BBD%7D%7B%20BQ%7D%20)
Which gives;
![\mathbf{\frac{y}{z}} = \frac{BD }{ BD - Q D}](https://tex.z-dn.net/?f=%20%5Cmathbf%7B%5Cfrac%7By%7D%7Bz%7D%7D%20%20%3D%20%20%5Cfrac%7BBD%20%7D%7B%20BD%20%20-%20Q%20D%7D%20)
![\frac{z}{y} = \frac{BD - QD }{ BD } = 1 - \frac{Q D }{ BD}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bz%7D%7By%7D%20%20%3D%20%20%5Cfrac%7BBD%20-%20QD%20%7D%7B%20BD%20%7D%20%20%3D%20%20%201%20-%20%5Cfrac%7BQ%20D%20%7D%7B%20BD%7D)
QD × x = BD × z
BD × z = (1 - QD/BD) × y = y - (QD × y/BD)
Therefore;
BD × z = y - (QD × y/BD)
BQ × y = y - (QD × y/BD)
BQ × y = y - (z × y/x) = y × (1 - z/x)
(1 - z/x) = BQ
BD × z = y × (1 - z/x)
BD = (y × (1 - z/x))/z
Therefore;
QD × x = y × (1 - z/x)
(BD-BQ) × x = y × (1 - z/x)
(BD-(1 - z/x)) × x = y × (1 - z/x)
BD = (y × (1 - z/x))/x + (1 - z/x)
BQ + QD = (1 - z/x) + (y × (1 - z/x))/x
BD = BQ + QD
(y × (1 - z/x))/x + (1 - z/x) = (y × (1 - z/x))/z
(1 - z/x)×(y/x + 1) =(1 - z/x) × y/z
Dividing both sides by (1 - z/x) gives;
y/x + 1 = y/z
Dividing all through by y gives;
(y/x + 1)/y = (y/z)/y
Therefore;
![\frac{1}{x} + \frac{1}{y}= \frac{1}{z}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7Bx%7D%20%20%2B%20%20%5Cfrac%7B1%7D%7By%7D%3D%20%20%20%5Cfrac%7B1%7D%7Bz%7D)
Learn more about characteristics similar triangles here:
brainly.com/question/1799826
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Area = base x height
Area = 12 x 5 = 60 square units
Answer:
17/50.
Step-by-step explanation:
In order to write 34% as a fraction or mixed number in simplest form, the following calculation has to be done:
34% = 0.34 = 34/100
34/100 = 17/50
Thus, given that 17 is a prime number that cannot be divided by other number than 1 or 17, the simplest form to write 34% as a fraction is 17/50.
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