Question

7. a) The hypotenuse of right-angled triangle is 2 more than twice of one of the other side while the
third side is 13 more than half of the hypotenuse. Find the length of the median to the
hypotenuse. ​

Answer 1

Answer:

I hope it will help you thanks

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Answer 2

The length of the median will be 17 cm.

Step-by-step explanation:

Given,

Hypotenuse is 2 more than twice the one of the other side.

Let us consider the side BC be the other side and let its length be x cm.

So from the given condition the length of the hypotenuse will be 2x+2 cm.

Also given that , the third side is 13 more than half of the hypotenuse

So AB is the third side, hence length of AB will be,

$AB = \frac{1}{2} (2x+2)+ 13$

∴ AB = x +14 cm

According to the Pythagoras theorem,

$(AB)^{2} + (BC)^{2} = (AC)^{2}$

Substituting the values of AB, AC and BC we get ,

$(x+14)^{2} + x^{2} = (2x+2)^{2}$

Solving the equation we get,

$x^{2} + 28x+196+x^{2} =4x^{2}+8x+4$

$2x^{2} +28x+196=4x^{2} +8x+4$

$-2x^{2} +20x+192=0$

$2x^{2} -20x-192=0$

$x^{2} -10x-96=0$

Factorizing the equation,

$x^{2} -16x+6x-96=0\\\\x(x-16)+6(x=16)=0\\\\(x+6)(x-16)=0$

∴ x = -6 or 16 cm

The length cannot be negative so the value x = -6 will be rejected

∴ The value of x is 16 cm

Hence the length of BC is 16 cm

=> The length of median = Half of the length of the hypotenuse

∴ $BD = \frac{1}{2} (2x+2)\\\\BD = \frac{1}{2} (2)(x+1)\\\\BD = x + 1\\\\BD = 16 + 1\\\\BD = 17 cm$

Hence the length of the median is 17 cm