Triangles ABC and DEF are similar triangles. Use this fact

ostric16

ostric16

Answered question

2021-11-28

Triangles ABC and DEF are similar triangles. Use this fact to solve the exercise. Round to the nearest tenth.
Find the perimeter of triangle ABC.

Answer & Explanation

Befory

Befory

Beginner2021-11-29Added 19 answers

Concept used:
(1) Pythagoras theorem: In a right angle triangle
(Hypotenuse)2=(Perpendicular)2+(Base)2
(2) If two triangles are similar, their perimeter have the exact same ratio.
In right angle triangle DEF
(Hypotenuse)2=(Perpendicular)2+(Base)2
(DE)2=(EF)2+(FD)2
(DE)=(15)2+(6)2
=225+1296
=1521
DE=±1521
=±139
Side can't be negative so DE =39
By similar triangle property:
perimeter of DEFperimeter of ABC=DFAC=DEAB=EFBC


perimeter of DEF=39+36+15=90


perimeter of DEFperimeter of ABC=DFAC


90perimeter of ABC=3612


perimeter of ABC=90×1236


perimeter of ABC=30

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