Question

An isosceles right triangle has an area of 12cm² .find the length of its hypotenuse

Answer 1

$\textbf{Solution:}$

Both the perpendicular and base are equal in length.

So Area of triangle = 1/2 x b x h 

Let b = h = y

1/2 x y x y = 12

y² = 24

y = √24

y = 2√6 cm

So Perpendicular = Base = 2√6 cm

Now by Pythagoras theorem,

(2√6)² + (2√6)²

=> √ 24 + 24

=> √48

=> 4√3 cm

So required hypotenuse = $\textbf{4root3 cm}$.

$\textbf{Thank you!!}$

Answer 2

Isosceles right triangle

⇒ The base and the height have equal length

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STEP 1: Define x:

Let the base = x

∴ the height = x

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STEP 2: Find x:

Area of triangle = 1/2 x base x height

Given that area = 12cm², find x

1/2 (x) (x) = 12

x² = 24

x = √24

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STEP 3: Find hypotenuse:

We found that the length and height = √24

Use Pythagoras' Theorem, a² + b² = c², to find c

(√24)² + (√24)² = c²

c² = 24 + 24

c² = 48

c = √48

c = 6.93 cm

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Answer: The length of the hypotenuse is 6.93 cm