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2 years ago

Points E, D, and H are the midpoints of the sides of ΔTUV. UV=82, TV=106, and HD= 82. Find HE.

Mathematics

1 answer:

Kobotan [32]2 years ago

7 0

Answer:

Step-by-step explanation:

53/106 = x/82 similar triangles

x=41

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<u>58 units</u>

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3 years ago

W is the midpoint of VX and Z is the midpoint of VY . If XY=p and WZ=p–30, what is WZ?

juin [17]

$\large{ \tt{❃ \: EXPLANATION}} :$

You'll have to know : Mid-point theorem states that A straight line segment joining the mid-points of any two triangle is parallel to the third side and it is equal to half of the length of the third side.

We're provided : XY = p , WZ = p - 30 & we're asked to find out the value of WZ. For that , firstly we have to find out the value of p.

$\large{ \tt{❁ \: LET'S \: START }: }$

Set up an equation & solve for p :

$\large{ \bf{☄ \: p - 30 = \frac{1}{2} p }}$

$\large{ \tt{↦ \frac{1}{2} p = p - 30}}$

$\large{ \tt{↦ \frac{1}{2} p - p = - 30}}$

$\large{ \tt{↦ \frac{p - 2p}{2} = - 30 }}$

$\large{ \tt{↦p - 2p = - 60}}$

$\large{ \tt{ ↦ \: - p = - 60}}$

$\large{ \tt{↦p = 60}}$

The value of p is 60

$\large{ \tt{❇ \: REPLACING \: VALUE}} :$

$\large{ \tt{↬ \: wz = p - 30 = 60 - 30 = \boxed{\boxed{ \tt{30 }} }✔}}$

Hence , WZ = 30 .

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3 years ago

Points​ E, D, and H are the midpoints of the sides of ΔTUV. UV​=82, TV=106​, and HD= 82. Find HE.

Points E, D, and H are the midpoints of the sides of ΔTUV. UV=82, TV=106, and HD= 82. Find HE.