Question

an isosceles triangle has area of 12 cm square find the length of its hypotenuse

Answer 1

The length of the hypotenuse is $4\sqrt{3}$ cm.

Correct question:

An isosceles right-angled triangle has area of 12 cm². Find the length of its hypotenuse.

Concept to be used:

Area of a right-angled triangle is given by

Δ = $\dfrac{1}{2}$ * base * height

Step-by-step explanation:

Step 1 of 3:

Let, ABC be our required isosceles right-angled triangle whose AB (height) = BC (base) = a and AC (hypotenuse) = h.

(Refer to the attached image.)

Step 2 of 3:

By Pythagorean theorem, we have

$AB^{2}+BC^{2}=AC^{2}$

⇒ $a^{2}+a^{2}=h^{2}$

⇒ $2a^{2}=h^{2}$

⇒ $a^{2}=\dfrac{1}{2}h^{2}$ ... ... (1)

Step 3 of 3:

Since the area of the given triangle is 12 square cm, can write

$\dfrac{1}{2}$ × BC × AB = 12

⇒ $\dfrac{1}{2}$ × a × a = 12

⇒ $\dfrac{1}{2}$ × $a^{2}$ = 12

⇒ $a^{2}$ = 24

⇒ $\dfrac{1}{2}h^{2}$ = 24, [by (1)]

⇒ $h^{2}=48$

⇒ h = $4\sqrt{3}$

Final answer:

The length of the hypotenuse is $4\sqrt{3}$ cm.

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