Answer:
√(45x²-72x+53)
Step-by-step explanation:
When you insert diagonals, two right-angle triangles are formed.
To find the length of the diagonals, we put the rectangles into pythagorean theorem:
a²=b²+c²
a²=(6x-7)²+(3x+2)²
a²=36x²-84x+49 + 9x²+12x+4
a²=45x²-72x+53
a=√(45x²-72x+53)
Lengths of diagonals of the rectangle are [tex]\boldsymbol{11}[/tex] units, [tex]\boldsymbol{11}[/tex] units respectively.
To understand the calculations, check below.
A rectangle is a parallelogram in which each angle is a right angle.
Diagonals of a rectangle are equal.
[tex]WY=XZ[/tex]
[tex]6x-7=3x+2[/tex]
[tex]3x=9[/tex]
[tex]x=3[/tex]
So,
[tex]WY=6x-7\\WY=18-7\\WY=11\\XZ=3x+2\\XZ=9+2\\XZ=11[/tex]
So, lengths of diagonals are [tex]\boldsymbol{11}[/tex] units, [tex]\boldsymbol{11}[/tex] units respectively.
Find out more information about rectangle here:
https://brainly.com/question/15019502?referrer=searchResults
