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2 years ago

If VW≅VY, WX = s + 69, and XY = 4s, what is the value of s?

Mathematics

1 answer:

Katen [24]2 years ago

7 0

Answer:

s = 23

Step-by-step explanation:

1. VW ≅ VY is given.

2. XV ≅ VX as it is the same side.

3. ∠WVX ≅ ∠YVX as they are both 90°. ∠WVY is 180° as it is a straight line, so both ∠WVX and ∠YVX are exactly half of that.

Given those three things, you can say that ΔWVX ≅ ΔYVX. Because all corresponding parts of congruent triangles are also congruent, you can be sure that WX ≅ XY. Finally, using that information, you can write an equation and solve for s.

$s+69=4s\\s-s+69=4s-s\\69=3s\\\frac{69}{3}=\frac{3s}{3}\\s=23$

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In ∆ABC with m∠C = 90° the sides satisfy the ratio BC:AC:AB = 4:3:5. If the side with middle length is 12 cm, find: 1) The perim

olga55 [171]

*The side with the middle length is 12cm, therefore BC must be 12 cm

------------------------------------------------------------
Ratio
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BC:AC:AB
4 : 3 : 5

-----------------------------------------------------------
Find 1 share
-----------------------------------------------------------
Given that BC = 12 cm
4 shares = 12 cm
1 share = 12 ÷ 4 = 3cm

-----------------------------------------------------------
Find AC (4 shares)
-----------------------------------------------------------
3 shares = 3 x 3 = 9 cm
BC = 9cm

-----------------------------------------------------------
Find AB (5 shares)
-----------------------------------------------------------
5 shares = 5 x 3 = 15cm
AB = 15cm

------------------------------------------------------------
Length
-----------------------------------------------------------
BC : AC : AB
12cm : 9cm : 15cm

------------------------------------------------------------------
Perimeter
------------------------------------------------------------------
12 + 9 + 15 = 36cm

------------------------------------------------------------------
Answer: The perimeter is 36cm
------------------------------------------------------------------

------------------------------------------------------------------
Area
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1/2 x 9 x 12 = 54cm²

------------------------------------------------------------------
Answer: Area = 54cm²
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Given that the biggest ratio is AB
⇒AB is the hypotenuse
AB = 15 cm

------------------------------------------------------------------
Answer: Hypotenuse = AB = 15cm
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AnnyKZ [126]

Answer:

<h3> $\boxed{ \bold{ \boxed{ \sf{x = - 2}}}}$ </h3>

Step-by-step explanation:

$\sf{9 - 4x = 17}$

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⇒ $\sf{ \frac{ - 4x}{ - 4} = \frac{8}{ - 4}}$

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