Question

An isosceles right triangle has area 8 cm2. The length of its hypotenuse is
(A) V32 cm
(B) 116 cm
(C) 148 cm
(D) 124 cm​

Answer 1

Answer:

if it is an isosceles right triangle

then let its base and height be of X cm

area =base*height÷2

8=X*X÷2

8/2=X*X

X*X=16=4*4

X=4cm

hypotenuse =root(4*4+4*4)=root 32

so (a) is ur answer friend

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Answer 2

Answer:

A) $\sqrt{32}$ cm

Step-by-step explanation:

Remembering the properties of :

An isosceles triangle :

* Any two sides are equal.

An right angle triangle:

* One angle is of 90°

Pythagorous Properties:

$hypotenuse^{2}$ = $Base^{2}$ + $Perpendicular^{2}$

Area of triangle :

$\frac{1}{2}$ × base × perpendicular

Now, A/q,

Given ,

Area of triangle is 8 $cm^{2}$

We know,

let side of isosceles triangle is $x^{}$

$\frac{1}{2}$ × base × perpendicular = 8

∴  $\frac{1}{2}$ ×  $x^{}$ × $x^{}$  = 8

⇒ $\frac{1}{2}$ × $x^{2}$ = 8

⇒ $x^{2}$ = 8 × 2

⇒ $x^{2}$ = 16

∴  $x^{}$  = 4

Now using pythagorous property:

$hypotenuse^{2}$ = $Base^{2}$ + $Perpendicular^{2}$

⇒ $hypotenuse^{2}$  = $4^{2}$  + $4^{2}$  

⇒ $hypotenuse^{2}$ = 16 + 16

⇒ $hypotenuse ^{}$ = $\sqrt{32}$  

∴ The length of its hypotenuse is $\sqrt{32}$ cm

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