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

ANSWER

45.6cm to the nearest tenth.

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,

${w}^{2} + {42}^{2} = {62}^{2}$

${w}^{2} = {62}^{2} - {42}^{2}$

${w}^{2} = 2080$

${w} = \sqrt{2080}$

$w = 4 \sqrt{130}$

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