Question

The length of the diagonal of a rectangle are \[3x + 5\;\] and \[50 - 6x\] 50−6x. Find the length of each diagonal.

Answer 1

Hint: To find the length of each diagonal of the rectangle just equate the length of each diagonal given in the question. Then solve the linear equation in one variable such that we can find the value of x. at last for finding the length of each diagonal just put the calculated value of x in place of x.

Complete step-by-step answer:
Suppose the diagonal of rectangle is as drawn in the figure

Suppose the diagonals are AC and BD
The length of AC is \[3x + 5\;\] and the length of BD is \[50 - 6x\]
As lengths of diagonals of rectangles are equal
 \[AC = BD\]
On putting the value of AC and BD
 \[ \Rightarrow 3x + 5 = 50 - 6x\]
On simplifying the above equation we get
 \[ \Rightarrow 9x = 45\]
Or,
 \[ \Rightarrow x = 5\]
Now to find the length of diagonal just put the value of x in \[3x + 5\;\]
So,
⇒ Length of diagonal \[ = 15 + 5 = 20\] .
So, the correct answer is “20 units”.

Note: Here we noticed that we put only the value of x in \[3x + 5\;\] not in \[50 - 6x\] . So here we will get the same result or same value of length of diagonal either we put in \[50 - 6x\] or \[3x + 5\;\] because the length of diagonal is always the same.