Chapter 12.1, Problem 61STP

To determine

Find the length of the diagonal.

Answer to Problem 61STP

The length of the diagonal is $26$ cm.

Explanation of Solution

Given: It is given in the question that the length and width of a rectangle are in the ratio of $5:12$ and the area of the rectangle is $240c{m}^2$ .

Concept Used:

In this, use the concept of area of rectangle and the formula used will be $l\times b$ and also use the pythagoras theorem.

Calculation: The ratio of the sides are $5:12$ .

So, the sides be $5:12\Rightarrow 5\times 2:12\times 2=10:24$

  $\begin{array}{l}l\times b\\ 10\times 24\\ 240c{m}^2\end{array}$

So, it is clear that the sides be $10$ cm and $24$ cm.

Let x be the length of the diagonal.

  $\begin{array}{l}{a}^2+b^2=c^2\\ {10}^2+{24}^2=x^2\\ x^2=100+576\\ x=\sqrt{676}=26\end{array}$

Conclusion:

The value of x is $26$ cm.