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प्रश्न
Construct a right triangle in which the sides, (other than the hypotenuse) are of length 6 cm and 8 cm. Then construct another triangle, whose sides are `3/5` times the corresponding sides of the given triangle.
उत्तर
Given:
BC = 6 cm, AC = 8 cm
The triangle to be formed is to be right angled triangle.
Steps of construction:
1. Draw a line segment BC = 6 cm.
2. Draw a ray CN making an angle of 90° at C.
3. With C as centre, taking 8 cm as the radius make an arc at CN intersecting it at A. Join AB.
4. Now, ABC is the triangle whose similar triangle is to be drawn.
5. Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.
6. Locate 5 (Greater of 3 and 5 in `3/5` ) points B1, B2, B3, B4 and B5 on BX so that BB1= B1B2 = B2B3= B3B4 = B4B5
7. Join B5C and draw a line through B3 (Smaller of 3 and 5 in `3/5` ) parallel to B5C to intersect BC at C’.
8. Draw a line through C’parallel to the line CA to intersect BA at A’.
9. A’BC’ is the required similar triangle whose sides are `3/5` times the corresponding sides of ΔABC.
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संबंधित प्रश्न
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Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are `4/3 `times the corresponding side of ΔABC. Give the justification of the construction.
Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5
If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.
If the point P (6, 7) divides the segment joining A(8, 9) and B(1, 2) in some ratio, find that ratio
Solution:
Point P divides segment AB in the ratio m: n.
A(8, 9) = (x1, y1), B(1, 2 ) = (x2, y2) and P(6, 7) = (x, y)
Using Section formula of internal division,
∴ 7 = `("m"(square) - "n"(9))/("m" + "n")`
∴ 7m + 7n = `square` + 9n
∴ 7m – `square` = 9n – `square`
∴ `square` = 2n
∴ `"m"/"n" = square`
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