Advertisements
Advertisements
Question
Vertices of given triangles are taken in order and their areas are provided aside. Find the value of ‘p’.
| Vertices | Area (sq.units) |
| (p, p), (5, 6), (5, –2) | 32 |
Advertisements
Solution
Let the vertices be A(p, p), B(5, 6) and C(5, –2)
Area of a triangle = 32 sq. units
`1/2[(x_1y_2 + x_2y_3 + x_3y_1) - (x_2y_1 + x_3y_2 + x_1y_3)]` = 32
`1/2[(6"p" - 10 + 5"p") - (5"p" + 30 - 2"p")]` = 32
`1/2 [11"p" - 10 - 3"p" - 30]` = 32
11p – 10 – 3p – 30 = 64
8p – 40 = 64
8p = 64 + 40
⇒ 8p = 104
p = `104/8`
= 13
The value of p = 13
APPEARS IN
RELATED QUESTIONS
The diagonal of a rectangular plot is 34 m and its perimeter is 92 m. Find its area.
A rectangular plot of land measures 45 m x 30 m. A boundary wall of height 2.4 m is built all around the plot at a distance of 1 m from the plot. Find the area of the inner surface of the boundary wall.
The diagonals of a quadrilateral are 16 cm and 13 cm. If they intersect each other at right angles; find the area of the quadrilateral.
A wire when bent in the form of a square encloses an area of 484 m2. Find the largest area enclosed by the same wire when bent to from:
- An equilateral triangle.
- A rectangle of length 16 m.
The following diagram shows a pentagonal field ABCDE in which the lengths of AF, FG, GH, and HD are 50 m, 40 m, 15 m and 25 m, respectively, and the lengths of perpendiculars BF, CH and EG are 50 m, 25 m and 60 m respectively. Determine the area of the field.
The length of a rectangular verandah is 3 m more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter.
(i) Taking x as the breadth of the verandah, write an equation in x that represents the above statement
(ii) Solve the equation obtained in (i) above and hence find the dimensions of the verandah.
Two adjacent sides of a parallelogram are 24 cm and 18 cm. If the distance between the longer sides is 12 cm; find the distance between the shorter sides.
Find the area and the perimeter of a square with diagonal 24 cm. [Take √2 = 1.41 ]
Find the area of a quadrilateral field whose sides are 12m, 9m, 18m and 21m respectively and the angle between the first two sides is a right angle. Take the value of `sqrt(6)` as 2.5.
Find the area of the quadrilateral whose vertices are at (– 9, 0), (– 8, 6), (– 1, – 2) and (– 6, – 3)
