Question

A rectangle has a diagonal of 12 feet and length of 9 feet. What is ghye width of the rectangle, in simplified form? (No decimal Answers (

Answer 1

The width of the rectangle is;

`3\sqrt[]{7}\text{ ft}`

Here, we want to get the width of the rectangle

To do this, we need a pictorial representation

We have this as;

As we can see, the rectangle is divided into two equal right-triangles

We have represented the width by w

We can use Pythagoras' theorem to get the width

The square of the diagonal (the hypotenuse) is equal the sum of the squares of the two other sides

Thus, we have;

`\begin{gathered} 12^2=9^2+w^2 \\ 144=81+w^2 \\ w^2\text{ = 144-81} \\ w^2\text{ = 63} \\ w\text{ = }\sqrt[]{63} \\ w\text{ = 3}\sqrt[]{7}\text{ ft} \end{gathered}`