Question

Isosceles trapezoid ABCD has diagonals AC = 10x + 7 and BD = 2x + 41. Find the value of x.

Answer 1

10x + 7 = 2x + 41
8x + 7 = 41
8x = 34
x = 17/4

Answer 2

`x=(17)/(4)` .

Explanation:

It is given that ABCD is an isosceles trapezoid and it has diagonals AC = 10x + 7 and BD = 2x + 41.

We need to find the value of x.

We know that the diagonals of an isosceles trapezoid are equal.

`AC=BD`

`10x+7=2x+41`

`10x-2x=41-7`

`8x=34`

`x=(34)/(8)`

`x=(17)/(4)`

Hence the value of x is
`(17)/(4)`.