If triangle TLY is similar to triangle CHK, find LY

Mathematics

1 answer:

Zolol [24]2 years ago

7 0

Answer:

Therefore the Length LY is 35 unit.

Step-by-step explanation:

Given:

ΔTLY is Similar to ΔCHK

TL = 25

LY = 4x -1

CH = 10

HK = x + 5

To Find:

LY = ?

Solution:

Δ TLY ~ Δ CHK ........Given

If two triangles are similar then their sides are in proportion.

$\dfrac{TL}{CH} =\dfrac{LY}{HK} \textrm{corresponding sides of similar triangles are in proportion}\\$

Substituting the values we get

$\dfrac{25}{10} =\dfrac{4x-1}{x+5}\\\\\dfrac{5}{2} =\dfrac{4x-1}{x+5}\\\\5(x+5)=2(4x-1)\\5x+25=8x-2\\3x=27\\\\x=\dfrac{27}{3}=9\\\\x=9$

Substituting 'x' in LY we get

$LY=4\times 9 - 1=36-1=35\ unit$

Therefore the Length LY is 35 unit.

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If angle ABC is one degree less than three times angle ABD and angle DBC=47 find each measure

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Now, from the information given we can infer that there is a line BD that cuts angle ABC in two parts: angle ABD and angle DBC

⇒ Angle ABC = Angle ABD + Angle DBC

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Let angle ABD be x

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Substituting the values in the above equations

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