Question

What is the length of the diagonal of a rectangle whose sides are $6$and $8$ ?
$A)10$
$B)15$
$C)20$
$D)25$

Answer 1

Hint: First, we will make use of the rectangle’s length, breadth, and diagonal to solve the given problem. The length, breadth, and diagonal of the rectangles always form a right-angled triangle. Hence, we will analyze the given problem with a diagram and then we will use the Pythagoras theorem to find the length of the diagonal.

Complete step-by-step solution:
Since from the given that we have the length of the diagonal of a rectangle whose sides are $6$and $8$. Hence, we need to find the unknown length of the diagonal.
Let us fix the length of the rectangle $6cm$ and its breadth $8cm$ (there is no problem if we fix the breadth and length as different values) and also, we showed the diagonal is D in the above diagram.
Hence, we have $l = 8cm,b = 6cm$ and D as the diagonal.
Now as per the property of the rectangle, the length, breadth, and diagonal always form a right-angled triangle with the diagonal as the hypotenuses.
Hence applying the Pythagoras theorem, we have ${D^2} = {l^2} + {b^2}$
Further solving with the substituted values, we get ${D^2} = {l^2} + {b^2} \Rightarrow {D^2} = {8^2} + {6^2}$
Acting the square values, we have ${D^2} = 64 + 36$
Thus, we have the diagonal as ${D^2} = 100$
Taking the square root, we get ${D^2} = 100 \Rightarrow D = 10$
Therefore, the option $A)10$ is correct.

Note: A diagonal which always divides the rectangle into two congruent right-angled triangles. Since the two intersecting diagonals, on the other hand, divide the rectangle into four congruent triangles.
Since a rectangle has four sides, also the square has four sides but the only difference is that the square has all four sides of equal length.