Answer:
It is not a rhombus. Its actually kite.
[tex]Solution,\\PT = TR = 8[/tex] [Δ[tex]PST[/tex]≅Δ[tex]STR[/tex] [tex]and~PT=TR~as~PT~and~TR~are~corresponding~sides~of~congruent~triangles.][/tex]
[tex]In triangle QTR,\\QR^2 = QT^2+TR^2\\or, 13^2 = QT^2 + 8^2\\or, QT^2 = 169-64\\or, QT = \sqrt{105}[/tex]
The length of the QT of the rhombus, when the value of QR is 13 and the value of PT is 8, is 10.24 units.
Rhombus is a closed shaped quadrilateral polygon in which all the sides are equal and opposites sides are parallel also opposite angles are equal.
In the quadrilateral shown in the image, the length of PT is 8 units and the length of QR is 13 units.
In this kite figure, the value PT is equal to the TR,
PT=TR
8=TR
Now in the right angle triangle QTR the square of QR is equal to the sum of the square of QT and TR according to the Pythagoras theorem. Thus,
(QR)²=(TR)²+(QT)²
(13)²=(8)²+(QT)²
(QT)²=169-64
QT=√(105)
QT=10.24 units.
Thus, the length of the QT of the rhombus when the value of QR is 13 and the value of PT is 8, is 10.24 units.
Learn more about rhombus here;
https://brainly.com/question/20627264
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