Question

একটি সমকোণী ত্রিভুজের তিনটি বাহুর দৈর্ঘ্য (X-2) সেমি X সেমি এবং(X+2) সেমি ত্রিভুজের অতিভুজের দৈর্ঘ্য কত​

Answer 1

English Translation:

The length of the three sides of a right-angled triangle are ( x -2) cm, x cm and ( x + 2) cm. The value of x is:

The value of x = 8 cm.

Given:

First side = (x - 2) cm

Second side = x cm

Third side = (x + 2) cm

To find:

the value of x.

Solution:

as given, it is a right-angled triangle. It has:

base : x cm

perpendicular : (x-2) cm

hypotenuse : (x+2) cm

using Pythagoras Theorem, we know that

(hypotenuse)² = (base)² + (perpendicular)²

putting the values in the equation,

(x+2)² = x² + (x-2)²

using the identiteeies,

(a+b)² = a² + 2ab + b²

(a-b)² = a² - 2ab + b²

expanding the values using the identities,

⇒x² + 2*x*2 +2² = x² + x² - 2*x*2 +2²

⇒0 = -x² -4x - 4 +2x² -4x + 4

⇒x² -8x = 0

⇒x(x - 8) = 0

⇒x - 8 =0

⇒x =8

∴ the value of x = 8

the three sides are :

⇒(x-2) = 8-2

⇒6 cm

x = 8 cm

(x+2) = 8+2

⇒10 cm

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