Question

the measure of hypotenuse of a isosceles right angle triangle is 3√2, what is the measure of its equal side​

Answer 1

3 cm

Question states that the measure of the hypotenuse of a isosceles right angle triangle is 3√2 cm. & we're asked to Calculate the measure of its equal sides. We have:

• Hypotenuse of the isosceles right angle triangle is 3√2 cm.

• The sides other than hypotenuse of an isosceles triangle are equal.

Let the equal side of the isosceles triangle is x cm.

Now, According to the Pythagoras theorem, Here:

$\longrightarrow\rm\quad \Big\{H\Big\}^2 = \Big\{P\Big\}^2 + \Big\{B\Big\}^2$

• Hypotenuse = 3√2

• Equal sides = x cm

⠀

$\longrightarrow\rm\quad \Big\{3\sqrt{2}\Big\}^2 = x^2 + x^2$

$\longrightarrow\rm\quad 18 = 2x^2$

$\longrightarrow\rm\quad x^2 = \cancel\dfrac{18}{2}$

$\longrightarrow\rm\quad x^2 = 9$

$\longrightarrow\rm\quad x = \sqrt{9}$

$\longrightarrow\quad\underline{\boxed{\pmb{\frak{x = 3}}}}\;\bigstar$

⠀⠀

❝ Therefore, the measure of each equal side is 3 cm. ❞

Answer 2

Given : The measure of hypotenuse of a isosceles right angle triangle is 3√2 .

Need To Find : The other two sides of an Isosceles Triangle ?

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⠀⠀⠀☯︎ We've provided with the Hypotenuse of an Isosceles Right angled triangle and we know that the two sides of an Isosceles triangle are equal .

❍ Let's say that , equal sides of Triangle be a cm .

$\dag\:\pmb{\frak {\underline { As\:We\:Know\:that\:\::\:}}}$

$\qquad \bigstar \:\:\underline{\pmb { \cal{ \: \:\:PYTHAGORAS \:\:\:THEOREM \:\:}}}\:$

$\qquad \star\:\pmb{\underline {\boxed {\frak { \:\:\bigg( \: Hypotenuse \:\bigg)^2\:=\:\bigg( \:Base\:\bigg)^2\:+\:\bigg(\:Perpendicular \:\bigg)^2\:}}}}$

Where ,

• Perpendicular and Hypotenuse are Equal sides of Triangle &
• Hypotenuse of a Triangle is 3√2 cm .

$\qquad \dag\:\underline {\frak{ Substituting \:known \:Values \:in \:Given \:Formula \:\::\:}}$

$:\implies \sf \:\:\bigg\{ \: Hypotenuse \:\bigg\}^2\:=\:\bigg\{ \:Base\:\bigg\}^2\:+\:\bigg\{\:Perpendicular \:\bigg\}^2\:$

$:\implies \sf \:\:\bigg\{ \: 3\sqrt{2} \:\bigg\}^2\:=\:\bigg\{ \:a\:\bigg\}^2\:+\:\bigg\{\:a\:\bigg\}^2\:$

$:\implies \sf \:\:\bigg\{ \: 3\sqrt{2} \:\bigg\}^2\:=\:\bigg\{ \:a^2\:+\:a^2\:\bigg\}\:$

$:\implies \sf \:\:\bigg\{ \: 3\sqrt{2} \:\bigg\}^2\:=\:\bigg\{ \:2a^2\:\:\bigg\}\:$

$:\implies \sf \:\:18\:=\: \:2a^2\:\:\:$

$:\implies \sf \:\:a^2\:=\: \cancel {\dfrac{18}{2}}\:\:$

$:\implies \sf \:\:a^2\:=\: \:9\:\:\:$

$:\implies \sf \:\:a\:=\: \:\sqrt{\bigg( \: 9 \:\bigg)}\:\:\:$

$:\implies \pmb {\underline {\boxed {\purple {\:\frak{ \:a\:\:=\:3\:cm\:}}}}}\:\bigstar \:$

∴ Hence ,  The equal sides of an Isosceles Right angled triangle is 3 cm .