Question

The hypotenuse of a right angled triangle is 20cm.the difference between its other two sides be 4cm.The sides are

Answer 1

Let one of the sides be x then another side is 4 + x

Applying Pythagoras theorem

(20)² = (x)² + (x + 4)²
400 = x² + x² + 8x + 16
400 = 2x² + 8x + 16
2x² + 8x - 384 = 0
x² + 4x - 192 = 0
x² + 16x - 12x - 192 = 0
x(x + 16) - 12(x + 16) = 0
(x - 12)(x + 16) = 0

x= 12 or x = -16
But length can't be negative.

So one of the side is 12 cm while the other is 16 cm

You can verify this too!
(12)² + (16)² = 144 + 256 = 400
Hypotenuse = √400 = 20 cm

Hope This Helps You!

Answer 2

Hi there !!

Let one of the sides be "x",

then another side is 4 + x

According to Pythagoras Theorem :

(20)² = (x)² + (x + 4)²

400 = x² + x² + 8x + 16

400 = 2x² + 8x + 16

2x² + 8x - 384 = 0

x² + 4x - 192 = 0

x² + 16x - 12x - 192 = 0

x(x + 16) - 12(x + 16) = 0

(x - 12) (x + 16) = 0


So ,

So the sides are 12 and 16 !!

12² + 16² = 144 + 256 = 400

20² = 400

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