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# 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. Q.7

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Sir give me the best and simple way to solve the problem of question from class 10th ncert of constructions chapter of exercise 11.1 of question no.7, how i solve this problem 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.

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1. The sides other than hypotenuse are of lengths 4cm and 3cm. It defines that the sides are perpendicular to each other

Construction Procedure:

The required triangle can be drawn as follows.

1. Draw a line segment BC =3 cm.

2. Now measure and draw âˆ = 90Â°

3. Take B as centre and draw an arc with the radius of 4 cm and intersects the ray at the point B.

4. Now, join the lines AC and the triangle ABC is the required triangle.

5. Draw a ray BX makes an acute angle with BC on the opposite side of vertex A.

6. Locate 5 such as B1, B2, B3, B4, on the ray BX such that such that BB1 = B1B2 = B2B3= B3B4 = B4B5

7. Join the points B3C.

8. Draw a line through B5 parallel to B3C which intersects the extended line BC at Câ€™.

9. Through Câ€™, draw a line parallel to the line AC that intersects the extended line AB at Aâ€™.

10. Therefore, Î”Aâ€™BCâ€™ is the required triangle.

Justification:

The construction of the given problem can be justified by proving that

Since the scale factor is 5/3, we need to prove

Aâ€™BÂ = (5/3)AB

BCâ€™ = (5/3)BC

Aâ€™Câ€™= (5/3)AC

From the construction, we get Aâ€™Câ€™ || AC

In Î”Aâ€™BCâ€™ and Î”ABC,

âˆ´ âˆ  Aâ€™Câ€™B = âˆ ACB (Corresponding angles)

âˆ B = âˆ B (common)

âˆ´ Î”Aâ€™BCâ€™ âˆ¼ Î”ABC (From AA similarity criterion)

Since the corresponding sides of the similar triangle are in the same ratio, it becomes

Therefore, Aâ€™B/AB = BCâ€™/BC= Aâ€™Câ€™/AC

So, it becomes Aâ€™B/AB = BCâ€™/BC= Aâ€™Câ€™/AC = 5/3

Hence, justified.

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