Question

In the figure below, GRAH is a rectangle, RA=7, and GA=10. Determine AH.

Answer 1

it's the square root of 51 which cannot be simplified

Explanation:

so put it like this $\sqrt{51}$ AoPS Problem

Answer 2

7.14 to the nearest hundreth

Explanation:

Using the Pythagorean Theorem,

`GA^(2) = ^(2) + AH^(2)`

From the question,

GA=10

RA=7

Also, RA is parallel and equal to GH.

This implies that, RA=GH=7

By substitution we obtain,

`^(2) = ^(2) + ^(2)`

`\implies 100=49 + ^(2)`

Subtracting 49 from both sides.

`\implies 100 - 49=49 - 49+ ^(2)`

`\implies ^(2) = 51`

Taking positive square root of both sides.

`\implies AH = √(51)`

`\implies AH =7.14`