The perpendicular bisector of side AB of ∆ABC intersects side BC at point D. Find AB if the perimeter of ∆ABC is with 12 cm larger than the perimeter of ∆ACD.
Answers
Answer:
Hence, AB=12.
Step-by-step explanation:
We are given that the perpendicular bisector of side AB of ∆ABC intersects side BC at point D.
this means that side AE=BE.
Also we could clear;ly observe that
ΔBED≅ΔAED
( since AE=BE, side ED common, ∠BED=∠AED
so by SAS congruency the two triangles are congruent)
Now we are given that:
the perimeter of ∆ABC is 12 cm larger than the perimeter of ∆ACD.
i.e. AB+AC+BC=AC+AD+CD+12
AB+BC=AD+CD+12
as AD=BD
this means that AD+CD=BD+CD=BC
AB+BC=BC+12
AB=12
Hence AB=12
Answer:
The required length of [tex]AB[/tex] is [tex]12\rm\;{cm}[/tex].
Step-by-step explanation:
Given: The perpendicular bisector of side [tex]AB[/tex] of [tex]\bigtriangleup{ABC}[/tex] intersects side [tex]BC[/tex] at point [tex]D[/tex] and the perimeter of [tex]\bigtriangleup{ACD}[/tex].
From the figure,
[tex]AE=BE[/tex] .......(1) (as [tex]DE[/tex] is perpendicular bisector of side [tex]AB[/tex])
Now, In [tex]\bigtriangleup{BED}[/tex] and [tex]\bigtriangleup{AED}[/tex]
[tex]AE=BE[/tex] ( from equation 1 )
[tex]\angle {BED} =\angle {AED}[/tex] ( Both [tex]90^\circ[/tex] )
[tex]ED=ED[/tex] ( Common side)
[tex]\bigtriangleup{BED}\cong\bigtriangleup{AED}[/tex] ( by SAS congruence rule)
[tex]BD=AD[/tex] .........(2) (by CPCT)
As per question,
The perimeter of ∆ABC is with 12 cm larger than the perimeter of ∆ACD.
[tex]AB+BC+AC=AC+CD+AD+12[/tex]
[tex]AB+BC=AD+CD+12\\AD+CD=BD+CD\\AB+BC=BC+12\\[/tex]
[tex]AB=12\rm\;{cm}[/tex]
Hence, the length of [tex]AB[/tex] is [tex]12\rm\;{cm}[/tex].
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First, notice that the quadratic expression in the numerator can be factored into (x + 6)(x - 4).
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We can now simplify the expression by canceling out the common factor of (x + 6):
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Answers
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Solution:
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Point=(h,t)→Point=(0,32)=(0,b)→b=32
For the next few hours, the temperature drops 2 degrees every hour. This represents the slope of the line (m): m=-2, negative because the temperature drops.
Slope-Intercept form:
y=mx+b; y=t, m=-2, x=h, b=32
Replacing the values:
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Answer:
t=-2h+32
Step-by-step explanation:
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