Question

Find 'x' and 'y' from the following figure.​

Answer 1

Question :

Find 'x' and 'y' from the following figure.​

Solution :

At first in ΔABD, ∠ADB = 90°. So ΔABD is a right triangle.

In ΔABD, using pythagoras theorem,

$\longmapsto\bold{Hypotenuse^2 = Base^2 + Altitude^2} \\\\ \\ \longmapsto\sf AB^2 = BD^2 + AD^2 \\\\ \\ \longmapsto\sf 13^2 = 5^2 + x^2 \\\\ \\ \longmapsto\sf 169 = 25 + x^2 \\\\ \\ \longmapsto\sf x^2 = 169 - 25 \\\\ \\ \longmapsto\sf x^2 = 144 \\\\ \\ \longmapsto\sf x = \sqrt{144} \\\\ \\ \longmapsto\underline{\boxed{\bold{x = 12 }}} \qquad\qquad\bigg\lgroup\bold{Required \ answer} \bigg\rgroup$

Now in ΔACD, ∠ADC = 90°. So it's also a right triangle.

Using pythagoras theorem,

$\longmapsto\bold{AC^2 = CD^2 + AD^2} \\\\ \\ \longmapsto\sf y^2 = 9^2 + x^2 \\\\ \\ \longmapsto\sf y^2 = 81 + 12^2 \\\\ \\ \longmapsto\sf y^2 = 81 + 144 \\\\ \\ \longmapsto\sf y^2 = 225 \\\\ \\ \longmapsto\sf y = \sqrt{225} \\\\ \\ \longmapsto\underline{\boxed{\bold{y = 15 }}} \qquad\qquad\bigg\lgroup\bold{Required \ answer}\bigg\rgroup$

$\therefore\underline{\boxed{\textsf{Required values of x and y are {\textbf{12 and 15}} respectively.}}}$

Answer 2

Step-by-step explanation:

HOPE IT HELPS BUDDY......