Question

A rectangle measures x by 10. The length of a diagonal of the rectangle is 2cm greater than the longer side x. Find x by forming an equation and solving it.

Answer 1

24 cm

Explanation:

We have the following:

shortest side: 10 cm

longest side: x

diagonal: x + 2

we can calculate the diagonal by means of pythagoras and it would be:

(x + 2) ^ 2 = 10 ^ 2 + x ^ 2

We solve this and we are left with:

x ^ 2 + 4 * x + 2 ^ 2 = 100 + x ^ 2

4 * x +4 = 100

x = (100-4) / 4

x = 24

which means that the longest side is 24 cm.