Question

The side of a right angle triangle is 17 cm less than the other side. If length of hypoter
25 cm, find the length of both sides.p
​

Answer 1

Given: The side of a right angle triangle is 17 cm less than the other side. length of hypotenuse is 25 cm

To Be Found: The length of the other sides.

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❒ Let the side AB be x and the side Bc be x - 17 respectively.

${ \underline{ \bigstar{ \boldsymbol{ According \: to \: the \: question : }}}}$

• The measure of the hypotenuse is 25cm , and now we have to find the lengths of the other 2 sides using suitable properties.

${ \underline{ \underline{ \red{ \rm {Pythagoras \: therom : }}}}}$

★ Pythagoras therom states that the square if hypotenuse equal to the sum of the squares of the other two sides.

${ \underline{ \frak{As \: we \: know \: that \dag}}}$

$\: \: \: \: \: \: \: \: \: \dag{ \bigg( \rm {Hypotenuse}^{2} = {Base}^{2} + {Side}^{2} } \bigg)$

Where,

• ➱ Hypotenuse = 25cm
• ➱ Base = X - 17
• ➱ Side = X

Here,

${ : \implies}{ \bf{ {(AC)}^{2} = {(AB)}^{2} + {(BC)}^{2} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} { \bf{ {(25)}^{2} = {(x)}^{2} + {(x - 17)}^{2} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies}\bf \: 625 = {x}^{2} + {x}^{2} - 2(x)(17) + {17}^{2} \\ \\ \\ { : \implies} \bf625 = {2x}^{2} - 34x + 289 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \bf 2 {x}^{2} - 34x + 289 - 625 = 0 \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \bf 2{x}^{2} - 34x - 336 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Fractorising The quadratic equation,

${ : \implies} \bf 2 {x}^{2} - 34x - 336 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \bf 2 {x}^{2} + 14x - 48x - 336 = 0 \\ \\ \\ { : \implies} \bf 2x(x + 7) - 48(x + 7) \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \bf (2x - 48)(x + 7) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Finding Roots :

Case-----(1)

★2x - 48 = 0

★2x = 48

★x = 24

Case-----(2)

★ x + 7 = 0

★ x = 0 - 7

★ x = -7

We know that,

• ↝ Height can't be negetive, so x = 24cm

Now,

• The other side = x - 17 = 24 - 17 = 7cm

Therefore,

${\boxed{\boxed{\rm{The\: other \:2 \:sides \:are \:24\: cm \:and \:7cm }}}}$

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Answer 2

Answer :

• The Other two sides is 24cm and 7cm

Given :

• The side of a right angle triangle is 17cm less than the other side
• Length of hypotenuse = 25cm

To find :

• Length of both sides

Solution :

• Let the base of right angle triangle be xcm
• Other be (x - 17cm)

And also Given that,

• Hypotenuse = 25cm

As we know that, Pythagoras theorem:

• (b)² + (p)² = (h)²

where, b is base xcm , p is perpendicular (x - 17)cm and h is hypothenuse 25cm

》(b)² + (p)² = (h)²

》(x)² + (x - 17)² = (25)²

》x² + x² - 34x + 289 = 625

》2x² - 34x + 289 = 625

》2x² - 34x - ( 625 - 289 ) = 0

》2x² - 34x - 336 = 0

》2x² + 14x - 48x - 336 = 0

》2x(x + 7) - 48(x + 7) = 0

》(x + 7)(2x - 48) = 0

Then

》x + 7 = 0

》x = 0 - 7

》x = - 7

》2x - 48 = 0

》2x = 48

》x = 48/2

》x = 24

• Side of triangle can't be negative then side = 24cm
• Other side = (x - 17) = 24 - 17 = 7cm

Hence , Other two sides is 24cm and 7cm