Question

plz answer this question​

Answer 1

Explanation:

In triangle ABD,

We know that AD = x and BD = 3x .

Let the longer side be y.

We want to find the ratio x : y or y : x. Hence, first we must calculate y.

Triangle ADB is a right angled triangle, for ∠DAB = 90° [∵ all angles of a rectangle are right angles].

This means that, by the Pythagoras theorem, which states that $c^2 = a^2 + b^2$ where c is the hypotenuse while a and b are the base and the height,

$BD^2=AD^2 + AB^2$

==> $(3x)^2 = x^2 + y^2$

==> $9x^2 =x^2 + y^2$

==> $y^2 = 9x^2-x^2$

==> $y^2=8x^2$

∴ $y = \sqrt{8x^2}=\sqrt8x=2\sqrt2 x$

Hence, $x:y=x:2\sqrt2x=1:2\sqrt2$

Answer: 1 : 2√2

I hope this helps. :D