Question

(5) If the area of the triangle with vertices
(a, 5), (6, 7) and (2, 3) is 10, then
a =
.. (a > 0).​

Answer 1

Answer:

area of triangle

$area = \frac{1}{2} (a \times (7 - 3) + 6 \times (3 - 5) + 2 \times (5 - 7)) \\ 10 = \frac{1}{2} \times (4a - 12 - 4) \\ 20 = 4a - 16 \\ 4a = 36 \\ a = 9$

Answer 2

Answer:

Value of a is equal to 9.

Step-by-step explanation:

The formula for the area of the triangle is given by $Area=\frac{1}{2} [x_{1} (y_{2}-y_{3})+x_{2} (y_{3}-y_{1})+x_{3} (y_{1}-y_{2})]$ where, $(x_{1},y_{1})$, $(x_{2},y_{2})$ and $(x_{3},y_{3})$ are the coordinates of the three vertices of the triangle.

A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees

The meeting point of a pair of sides is called its vertex.

Any of a set of numbers used in specifying the location of a point is called coordinates.

Here it is given that the area of a triangle with vertices (a,5), (6,7) and (2,3) is 10.

We should find the value of a.

The value of a can be found by substituting the coordinates in the area of triangle formula and solving for a.

$Area=\frac{1}{2} [a (7-3)+6 (3-5)+2 (5-7)]$

$10=\frac{1}{2} [a (4)+6 (-2)+2 (-2)]$

$10*2= 4a-12-4$

$20=4a-16$

$20+16=4a$

$36=4a$

$a=\frac{36}{4}=9$

The value of a is 9.

To know more about triangle go to the following link.

brainly.in/question/17424774

To know more about area go to the following link.

brainly.in/question/48376175

#SPJ6