Question

in rectangle QRST , QS = 3x+7 and RT = 5X-3.find the lengths of the diagonals of QRSTeach diagonal has a length of ....... units.

Answer 1

Consider the rectangle drawn below,

Consider the properties of rectangle that the opposite sides are equal, and both the diagonals are also equal in length.

$QS=RT\Rightarrow3x+7=5x-3\Rightarrow5x-3x=7+3\Rightarrow2x=10\Rightarrow x=5$

Thus, the value of 'x' is 5.

Substitute the value to obtain the diagonal QS as,

$QS=3(5)+7=15+7=22$

Similarly solve for the diagonal RT as,

$RT=5(5)-3=25-3=22$

Already we knew that the diagonal will be equal with the length 22 units.