Question 700674
: how do you find the length of a diagonal of a rectangle if all you have is an equation: 7x-2 for one diagonal and 4x+3 for the other diagonal?
:
We know that the two diagonals in rectangle are equal, therefore
7x - 2 = 4x + 3
Solve for x
7x - 4x = 3 + 2
3x = 5
x = 5/3
:
Find the length of the diagonal by replacing x with 5/3 in 7x - 2
d = 7(5/3) - 2
d = (35/3) - 2
d = 11{{{2/3}}} - 2
d = 9{{{2/3}}} is the length of the diagonal
:
Check this by doing the same in 4x + 3
d = 4(5/3) + 3
d = (20/3} + 3
d = 6{{{2/3}}} + 3
d = 9{{{2/3}}}