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Draw a right triangle in which the sides...

Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are `5/3` times the corresponding sides of the given triangle.

Text Solution

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Steps of Construction :
1. Draw a line segment BC = 4 cm.
2. From B. draw a line AB = 3 cm which making right angle at B.
3. Join `AC. DeltaABC` is the given right triangle.
4. From B, draw an acute `angleCBY` downwards.
5. On BY, take five points `B_(1),B_(2),B_(3),B_(4)andB_(5)` such that`BB_(1)=B_(1)B_(2)=B_(2)B_(3)=B_(3)B_(4)=B_(4)B_(5).`
6. Join `B_(3)C.`
7. From point `B_(5),` draw `B_(5)C'"||"B_(3)C` producijng BC to C'.
8. Form point C', draw `C'A"||"CA` producing BA to A' Hence, `DeltaA'BC'` is the required triangle.
Justification :
By construction, `B_(5)C'"||"B_(3)C`
`therefore" "(BC)/(C C')-3/2`
`Now," "(BC')/(BC)=(BC+C C')/(BC)=1+(C C')/(BC)=1+2/3=5/3`
`Also," "C'A'"||"CA`
`therefore" "DeltaABC~DeltaA'BC'`
`and" "(A'B)/(AB)=(BC')/(BC)=(A'C')/(CA)=5/3.`
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