Question

The diagonal of the rectangle is equal to 34 cm. If the breadth of the rectangle is equal to 16 cm; find the length in cm.

Answer 1

Hint:We know that if the length of the rectangle is equal to l and breadth of the rectangle is equal to b and the length of diagonal is equal to d, then we get \[d=\sqrt{{{l}^{2}}+{{b}^{2}}}\]. By using this concept, we can find the length of the rectangle if we know that diagonal of the rectangle and the breadth of the rectangle.

Complete step by step answer:
From the question, it is given that the diagonal of the rectangle is equal to 34 cm and the breadth of the rectangle is equal to 16 cm.
We know that if the length of the rectangle is equal to l and breadth of the rectangle is equal to b and the length of diagonal is equal to d, then we get \[d=\sqrt{{{l}^{2}}+{{b}^{2}}}\].

Let us consider
\[\Rightarrow d=\sqrt{{{l}^{2}}+{{b}^{2}}}....(1)\]
From the question, we get the value if d is equal to 34 and the value of b is equal to 16 cm.
\[\begin{align}
  & \Rightarrow d=34....(2) \\
 & \Rightarrow b=16....(3) \\
\end{align}\]
Now we will substitute equation (2) and equation (3) in equation (1), then we get
\[\Rightarrow 34=\sqrt{{{l}^{2}}+{{16}^{2}}}\]
Now by squaring on both sides, then we get
\[\begin{align}
  & \Rightarrow 1156={{l}^{2}}+256 \\
 & \Rightarrow {{l}^{2}}=900 \\
 & \Rightarrow l=30....(4) \\
\end{align}\]
Now from equation (4), it is clear that the value of l is equal to 30. So, we can say that the value of the length of a rectangle is equal to 30 if the breadth of a rectangle is equal to 16 and the diagonal of a rectangle is equal to 34.
Note:
Some students may have misconceptions that if the length of the rectangle is equal to l and breadth of the rectangle is equal to b and the length of diagonal is equal to d, then we get \[l=\sqrt{{{d}^{2}}+{{b}^{2}}}\]. If this misconception is followed, then we cannot get the correct value of l. So, this misconception should be avoided. Students can always consider a right-angled triangle because the diagonal divides the rectangle into equal triangles and all angles of the rectangle are right angles. Then they can apply Pythagoras Theorem to avoid this misconception.