Step 1We have to find the value of x and y.Step 2In&nbsp;△ABC,DE∣∣BC&nbsp;and&nbsp;AD=BDWe have ,AD=3y,BD=12y+20,AE=20−3x&nbsp;and&nbsp;CE=2x−5if&nbsp;DE∣∣BC&nbsp;and&nbsp;DE=12BCThen,AD=BD&nbsp;and&nbsp;AE=CEFor,AD=BD⇒3y=12y+20⇒3y−12y=20⇒6y−y2=206y−y=405y=40y=405⇒y=8For,AE=CE⇒20−3x=2x−5⇒20+5=2x+3x⇒5x=25⇒x=255⇒x=5Hence,x=5 and y=8

Question: "Find x and y"

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

Jayleen Aguirre

Answered question

2022-04-05

Find x and y

Answer & Explanation

Kaitlynn Craig

Beginner2022-04-06Added 13 answers

Step 1
We have to find the value of x and y.

Step 2
In $△ A B C, D E ∣ ∣ B C$ and $A D = B D$
We have , $A D = 3 y, B D = \frac{1}{2} y + 20, A E = 20 - 3 x$ and $C E = 2 x - 5$
if $D E ∣ ∣ B C$ and $D E = \frac{1}{2} B C$
Then, $A D = B D$ and $A E = C E$
For, $A D = B D$
$\Rightarrow 3 y = \frac{1}{2} y + 20$
$\Rightarrow 3 y - \frac{1}{2} y = 20$
$\Rightarrow \frac{6 y - y}{2} = 20$
$6 y - y = 40$
$5 y = 40$
$y = \frac{40}{5}$
$\Rightarrow y = 8$
For, $A E = C E$
$\Rightarrow 20 - 3 x = 2 x - 5$
$\Rightarrow 20 + 5 = 2 x + 3 x$
$\Rightarrow 5 x = 25$
$\Rightarrow x = \frac{25}{5}$
$\Rightarrow x = 5$
Hence,x=5 and y=8

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