IF IN AN ISOSCELES TRAPEZIUM,DIAGONAL AC=(8X-7)CM AND DIAGONAL BD=(5X+2)CM,THEN FIND THE LENGTH OF AC ?
As in isosceles trapezium diagonal ate equal
So
8x-7=5x+2
3x=9
X =3
So AC is = 8x-7= 8*3-7
=17cm
since the figure is isosceles, the diagonals are equal. So,
8x-7 = 5x+2
Now, just solve for x and evaluate the length.
To find the length of AC in an isosceles trapezium, we can set up an equation using the given information.
In an isosceles trapezium, the diagonals are congruent. Therefore, we can equate the two expressions for the diagonals: AC = BD.
Given: AC = (8x - 7) cm and BD = (5x + 2) cm.
Setting up the equation:
(8x - 7) = (5x + 2)
Now, solve for x by simplifying and isolating x:
8x - 7 = 5x + 2
8x - 5x = 2 + 7
3x = 9
x = 3
Now that we have the value of x, we can substitute it back into one of the expressions to find the length of AC. Let's use the expression for AC:
AC = (8x - 7) = (8 * 3 - 7) cm
AC = (24 - 7) cm
AC = 17 cm
Therefore, the length of AC in the isosceles trapezium is 17 cm.