given that rectangle MNOP ~ rectangle STUV, what is the length of TU

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The value of x or the length of TU is 22.5.What is a rectangle?That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.Since all the rectangles are similar, therefore, the corresponding sides of the rectangle will be in ratio. Therefore,[tex]\dfrac{\text{Length of STUV}}{\text{Length of MNOP}} = \dfrac{9}{6}[/tex]Similarly, the breadth will be,[tex]\dfrac{\text{Width of STUV}}{\text{Width of MNOP}} = \dfrac{\text{Length of STUV}}{\text{Length of MNOP}}\\\\\\\dfrac{\text{Width of STUV}}{\text{Width of MNOP}} = \dfrac{9}{6}\\\\\\\dfrac{x}{15}=\dfrac96\\\\\\x = \dfrac{9 \times 15}{6} = 22.5[/tex]Hence, the value of x or the length of TU is 22.5.Learn more about Rectangle: