Question

A square measures 15 inches on its side. What is the length of its diagonal? (Round your answer to the nearest tenth.)

Answer 1

Let's draw the figure:

Cutting the other side, it appears to be a right triangle. Thus, to be able to get the length of its diagonal, we can use the Pythagorean Theorem.

`\text{ a}^2+b^2=c^2`
`\text{ c = }\sqrt[]{a^2+b^2}`

Let's substitute a and b by 15 since the figure is a square, thus, all of its sides are the same.

We get,

`\text{ c = }\sqrt[]{a^2+b^2}`
`\text{ c = }\sqrt[]{15^2+15^2}`
`\text{ c = }\sqrt[]{225\text{ + 225}}`
`c\text{ = }\sqrt[]{2\text{ x 225}}\text{ = }\sqrt[]{2x15^2}`
`\text{ c = 15}\sqrt[]{2}`

Therefore, the length of its diagonal is 15√2 inches.