Question

The diagonal length of a rectangular playing field is 76 feet, and its width is 48 feet. How long is the playing field?

Answer 1

The length of playing field is 58.9 feet

Solution:

Given that, the diagonal length of a rectangular playing field is 76 feet,  

And its width is 48 feet.  

To find: length of playing field

Now, we know that, diagonal, width and length of a rectangle will form an right angle triangle with diagonal as hypotenuse.

So, now, in a right angled triangle  we can use pythagorean theorem to find the length

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

By above definition, In a right angled triangle ABC we get

$c^2 = a^2 + b^2$

Where "c" is the length of hypotenuse

"a" is the length of one leg of right angled triangle

"b" is the length of other leg of right angled triangle

$\begin{array}{l}{\text {Then, diagonal = width }^{2}+\text { length }^{2}} \\\\ {76^{2}=48^{2}+\text {length }^{2}} \\\\ {\text {Length }^{2}=76^{2}-48^{2}} \\\\ {\text {Length }^{2}=5776-2304}\end{array}$

$\begin{array}{l}{\text { Length }^{2}=3472} \\\\ {\text { Length }=\sqrt{3472}} \\\\ {\text { Length }=58.92}\end{array}$

Hence, the length of the rectangular field is 58.9 feet