Question

in figure, BC=5cm angle B=90°
, AB=5AE, CD=2AE And AC=ED.CALCULATE THE LENGTHS OF EA, CD, AB, AC.
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Answer 1

Answer:

BC=5 cm

AE=x

• AB=5AE=5x => BE=5x-x=4x

• CD=2x

AB²+BC²=AC² => (5x)²+5²=AC²

BE²+BD²=ED² => (4x)²+(5+2x)²=ED²

AC=ED =>  

• (5x)²+5²=(4x)²+(5+2x)
• 25x²+25= 16x²+25+20x+4x²
• 5x²-20x=0
• x(x-4)=0
• x=4 cm

EA= 4 cm

CD= 2*4 cm= 8 cm

AB= 5*4 cm= 20 cm

AC= √(5*4)²+25= √425=5√17