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Mathematics

The hypotenuse of a right triangle is 20 m. If the difference between the lengths of other sides be 4 m, find the other sides.

Quadratic Equations

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Answer

Let the shorter side of right angled triangle = x.

Given,

Hypotenuse of triangle = 20 m

Difference between the other two sides of right angled triangle = 4 m

Then the longer side of right angled triangle (aprat from hypotenuse) = (x + 4) m.

By pythagoras theorem,

⇒ x2 + (x + 4)2 = 202

⇒ x2 + (x2 + 8x + 16) = 400

⇒ x2 + x2 + 8x + 16 - 400 = 0

⇒ 2x2 + 8x - 384 = 0

⇒ 2(x2 + 4x - 192) = 0

⇒ x2 + 4x - 192 = 0

⇒ x2 + 16x - 12x - 192 = 0

⇒ x(x + 16) - 12(x + 16) = 0

⇒ (x - 12)(x + 16) = 0

⇒ (x - 12) = 0 or (x + 16) = 0     [Using zero-product rule]

⇒ x = 12 or x = -16.

Since, length cant be negative.

∴ x = 12 m

Shorter side of right angled triangle = 12 m

Longer side of right angled triangle = x + 4 = 12 + 4 = 16 m.

Hence, length of two sides of right angled triangle is 12 m and 16 m.

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