d269909faa
* fix: clean-up Project Euler 381-400 * fix: missing image extension * fix: missing subscripts Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
47 lines
1021 B
Markdown
47 lines
1021 B
Markdown
---
|
|
id: 5900f4f21000cf542c510005
|
|
title: 'Problem 390: Triangles with non rational sides and integral area'
|
|
challengeType: 5
|
|
forumTopicId: 302055
|
|
dashedName: problem-390-triangles-with-non-rational-sides-and-integral-area
|
|
---
|
|
|
|
# --description--
|
|
|
|
Consider the triangle with sides $\sqrt{5}$, $\sqrt{65}$ and $\sqrt{68}$. It can be shown that this triangle has area 9.
|
|
|
|
$S(n)$ is the sum of the areas of all triangles with sides $\sqrt{1 + b^2}$, $\sqrt{1 + c^2}$ and $\sqrt{b^2 + c^2}$ (for positive integers $b$ and $c$) that have an integral area not exceeding $n$.
|
|
|
|
The example triangle has $b = 2$ and $c = 8$.
|
|
|
|
$S({10}^6) = 18\\,018\\,206$.
|
|
|
|
Find $S({10}^{10})$.
|
|
|
|
# --hints--
|
|
|
|
`nonRationalSidesAndIntegralArea()` should return `2919133642971`.
|
|
|
|
```js
|
|
assert.strictEqual(nonRationalSidesAndIntegralArea(), 2919133642971);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function nonRationalSidesAndIntegralArea() {
|
|
|
|
return true;
|
|
}
|
|
|
|
nonRationalSidesAndIntegralArea();
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
// solution required
|
|
```
|