Question

A rectangular painting by Leonardo da Vinci measured 62cm along its diagonal. If the painting has a height of 42 cm how wide is the painting?

Answer 1

45.6cm to the nearest tenth.

Step-by-step explanation

The diagonal of the rectangular painting is 62cm.

The height of the painting is 42 cm.

The height of the painting h , the diagonal, and the width of the painting forms a right triangle with the diagonal being the hypotenuse.

From the Pythagoras Theorem,

`{w}^(2) + {42}^(2) = {62}^(2)`

`{w}^(2) = {62}^(2) - {42}^(2)`

`{w}^(2) = 2080`

`{w} = √(2080)`

`w = 4 √(130)`

The width of the painting is 45.6cm to the nearest tenth.