Question

Find the value of x and y.
Given, $\angle DAC={90}^{\circ }$

• A. x = 26 m
• B. x = $\sqrt{26}$ m
• C. y = 10 m
• D. y = $\sqrt{10}$ m

Answer 1

Answer: (B), (D)

The correct options are
B x = $\sqrt{26}$ m
D y = $\sqrt{10}$ m

In $\Delta ABC$, hypotenuse = x m

Using Pythagoras Theorem,
we get,
$x^2=5^2+1^2$
$x^2=25+1=26$
$x=\pm \sqrt{26}$
$\therefore x=\sqrt{26}m$ as x > 0

In $\Delta ACD$, the hypotenuse is 6 m.

Using Pythagoras Theorem,
we get,
$y^2+(\sqrt{26}{)}^2=(6{)}^2$
$\Rightarrow y^2+26=36$
$\Rightarrow y^2=10$
$\Rightarrow y=\pm \sqrt{10}$
$\therefore y=\sqrt{10}m$, as y > 0