Question

Find the sides of the isosceles right angled triangle whose area is 200².

Answer 1

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Step-by-step explanation:

Answer 2

Answer:

1 ) base = 20 metres

2 ) altitude = 20 metres

3 ) hypotenuse= 28.28 metres

Step-by-step explanation:

( refer to image for diagram )

in an isosceles right angled triangle, the base and altitude are in equal length

so let altitude = base = "x"

we know that area of triangle = 1/2 * base * height

=> 1/2 * x * x = 200

=> x * x = 200 * 2

=> x² = 400

=> x = $\sqrt{400}$

= 20 metres

so altitude = base = 20 metres

let hypotenuse = "h"

we know that in a right angled triangle , altitude² + base² = hypotenuse² ( Pythagoras' Theorem )

so x² + x² = h²

=> ( 20 )² + ( 20 )² = h²

=> 400 + 400 = h²

=> h² = 800

=> h = $\sqrt{800}$

= $\sqrt{400 * 2}$

= 20 *  $\sqrt{2}$

= 28.28 ( approx )

therefore the

1 ) base = 20 metres

2 ) altitude = 20 metres

3 ) hypotenuse= 28.28 metres