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4 years ago

Which value of y would make OP || LN ?

Mathematics

1 answer:

guajiro [1.7K]4 years ago

3 0

Remark
All you need do is assume the small triangle is similar to the large one. MO:ML :: MP:MN must be solved.

Givens
MO = 28
ML = 28 + 14
MP = y
MN = y + 18

Equation
28:28+14 :: y: y + 18

Solve
28/42 = y / (y + 18)
28*(y + 18) = 42y Remove the brackets
28y + 18*28 = 42y
28y + 504 = 42y Subtract 28y from both sides.
504 = 42y - 28y
504 = 14y Divide by 14
504/14 = y
y = 36

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3 years ago

ABC and EDC are straight lines. EA is parallel to DB. EC = 8.1 cm. DC = 5.4 cm. DB = 2.6 cm. (a) Work out the length of AE. cm (

harkovskaia [24]

By applying the knowledge of similar triangles, the lengths of AE and AB are:

a. $\mathbf{AE = 3.9 $ cm}\\\\$

b. $\mathbf{AB = 2.05 $ cm} \\\\$

See the image in the attachment for the referred diagram.

The two triangles, triangle AEC and triangle BDC are similar triangles.
Therefore, the ratio of the corresponding sides of triangles AEC and BDC will be the same.

This implies that:

AC/BC = EC/DC = AE/DB

Given:

$EC = 8.1 $ cm\\\\DC = 5.4 $ cm\\\\DB = 2.6 cm\\\\AC = 6.15 $ cm$

a. Find the length of AE:

EC/DC = AE/DB

Plug in the values

$\frac{8.1}{5.4} = \frac{AE}{2.6}$

Cross multiply

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Divide both sides by 5.4

$AE = \frac{21.06}{5.4} = 3.9 $ cm$

b. Find the length of AB:

$AB = AC - BC$

AC = 6.15 cm

To find BC, use AC/BC = EC/DC.

Plug in the values

$\frac{6.15}{BC} = \frac{8.1}{5.4}$

Cross multiply

$BC \times 8.1 = 6.15 \times 5.4\\\\BC = \frac{6.15 \times 5.4}{8.1} \\\\BC = 4.1$

Thus:

$AB = AC - BC$

Substitute

$AB = 6.15 - 4.1\\\\AB = 2.05 $ cm$

Therefore, by applying the knowledge of similar triangles, the lengths of AE and AB are:

a. $\mathbf{AE = 3.9 $ cm}\\\\$

b. $\mathbf{AB = 2.05 $ cm} \\\\$

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3 years ago

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What about 35 min = ?

= 35 x 60

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3 years ago

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