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In right triangle ABC shown to the right, the lengths of AB, BC, and BE are 20, 15, and 6, respectively. What is the length of DE?

Sagot :

asuwafohjames

Answer:

12

Step-by-step explanation:

Assuming the diagram is thesame as the one attached,

From the diagram,

Triangle ABC is similar to Triangle DEC

ΔABC is similar to ΔDEC

Note: In similar triangle, ratio of corresponding sides are equal

Therefore,

line(AB) /line(DE) = line(BC)/line(EC).................... Equation 1

Given: AB = 20, BC = 15, EC = BC-BE = (15-6) = 9

Substitute these values into equation 1 and solve for Line DE

20/DE = 15/9

DE = (20×9)/15

DE = 12.

Hence line DE = 12.

View image asuwafohjames
okpalawalter8

Answer:

[tex]DE=12[/tex]

Step-by-step explanation:

From the question we are told that:

 [tex]AB=20\\\\BC=15\\\\BE =6[/tex]

Generally the equation for the similar triangles is mathematically given by

  [tex]\frac{AB}{BC} =\frac{DE}{EC}[/tex]

Where

 [tex]EC = BC - BE \\\\EC= 15-6 \\\\EC= 9[/tex]

Therefore

 [tex]\frac{20}{15} =\frac{DE}{9}[/tex]

 [tex]\frac{20*9}{15} =DE[/tex]

 [tex]DE=12[/tex]

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