Question

The length of the diagonal of the rectangle is $3x+5$ and $50-6x.$ Find length of each diagonal.

Answer 1

Hint: In this question we have to find the length of each diagonal, we will apply properties of the rectangle .We know that the length of two diagonals of a rectangle are always equal. It can be observed that lengths of diagonal are given in terms of $x$. Therefore, using simple algebraic expressions we will evaluate x and hence measurement of diagonal.

Complete step-by-step answer:
We are given with the length of diagonals as $3x+5$ and $50-6x$.
By properties of the rectangle, we know that diagonals of rectangle are equal in length.
Since, the diagonal of a rectangle are equal, we can write,
 $3x+5=50-6x$
Simplifying the above for determining the value of $x,$ we get
$3x-5=50-6x$
Taking the variable terms, that is terms containing $x$ to left hand side and number to right side, we get,
$3x+6x=50-5$
on simplification, we get,
$9x=45$
dividing both side by $9$,
$x=5$
Thus, we obtain the value of $x$ as $5$.
Now, we need to find the length of the diagonal for that purpose we need to substitute the value of $x$ in,
$50-6x$
Where we put $x=5$, we get,
Length of diagonal, $=50-6x$
Length $=50-6\times 5$
$=50-30=20$

therefore , the required length of diagonal is $20.$

Note:
Always remember the general properties of quadrilaterals as they are very useful in solving such questions and they will save your time as well.
Whenever values of any dimension are given in terms of any variable always try to determine the value of the variable first and then proceed to find out the actual value .
be very careful while applying algebraic operations a small error of sign can change the whole answer.