Advertisements
Advertisements
प्रश्न
If the area of triangle ABC formed by A(x, y), B(1, 2) and C(2, 1) is 6 square units, then prove that x + y = 15 ?
उत्तर
It is known that the area of a triangle whose vertices are (x1, y1), (x2, y2) and (x3, y3) is given by the numerical value of the expression `1/2[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]`
The vertices of ΔABC are given as A (x, y), B (1, 2) and C (2, 1) is given by
Area of ΔABC
`1/2[x(2-1)+1xx(1-y)+2(y-2)]`
`1/2[x+1-y+2y-4]`
`1/2[x+y-3]`
The area of ΔABC is given as 6.
`rArr 1/2[x+y-3]=6rArrx+y-3=12`
`thereforex+y=15`
APPEARS IN
संबंधित प्रश्न
The perimeter of a right triangle is 60 cm. Its hypotenuse is 25 cm. Find the area of the triangle.
Find the area of the quadrilateral ABCD whose vertices are respectively A(1, 1), B(7, –3), C(12, 2) and D(7, 21).
Find values of k if area of triangle is 4 square units and vertices are (k, 0), (4, 0), (0, 2)
Find the area of a triangle whose sides are respectively 150 cm, 120 cm and 200 cm ?
Show that the points are the vertices of an isosceles right triangle.
Prove that the points A(2, 4), b(2, 6) and (2 +`sqrt(3)` ,5) are the vertices of an equilateral triangle
For what value of k(k>0) is the area of the triangle with vertices (-2, 5), (k, -4) and (2k+1, 10) equal to 53 square units?
The table given below contains some measures of the right angled triangle. Find the unknown values.
| Base | Height | Area |
| 20 cm | 40 cm | ? |
Find the coordinates of the point Q on the x-axis which lies on the perpendicular bisector of the line segment joining the points A(–5, –2) and B(4, –2). Name the type of triangle formed by the points Q, A and B.
If area of a triangular piece of cardboard is 90 cm2, then the length of altitude corresponding to 20 cm long base is ______ cm.
