Question

The hypotenuse of a right triangle is 10cm long. If one leg is 2 units longer than the other leg, then how long is the longer leg?(M not leaving brainly.. still active don't worry!) ​

Answer 1

Answer:

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Answer 2

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

The hypotenuse of a right triangle is 10cm long. If one leg is 2 units longer than the other leg, then how long is the longer leg?

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{Given}}}}$

• The hypotenuse of a right triangle is 10cm long.
• If one leg is 2 units longer than the other leg .

$\Large{\underline{\mathfrak{\bf{Given}}}}$

• Length of longer leg /

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

Let,

• second leg = x.

A/C to question,

( one leg is 2 units longer than the other leg )

➠ first leg = (x+2).

So,

we can say that here,

• Base = (x+2)
• Perpendicular = x.

Pythagoras theorem

$\boxed{\underline{\tt{\red{\:(Hypotenuse)^2\:=\:(perpendicular)^2+(Base)^2}}}}$

So,

$:\mapsto\tt{\:(10)^2\:=\:(x+2)^2+x^2} \\ \\ :\mapsto\tt{\:(x^2+x^2+4x+4)\:=\:100} \\ \\ :\mapsto\tt{\:2x^2+4x-96\:=\:0} \\ \\ :\mapsto\tt{\:x^2+2x-48\:=\:0} \\ \\ :\mapsto\tt{\:x^2+8x-6x-48\:=\:0} \\ \\ :\mapsto\tt{\:x(x+8)-6(x+8)\:=\:0} \\ \\ :\mapsto\tt{\:(x-6)(x+8)\:=\:0} \\ \\ :\mapsto\tt{\:(x-6)\:=\:0\:\:Or\:(x+8)\:=\:0} \\ \\ :\mapsto\tt{\orange{\:x\:=\:6\:\:Or\:\:x\:=\:-8}}$

But, we know length is always positive .

So,

• x = -8 Negligible .

Then take ,

• x = 6

$\Large{\underline{\mathfrak{\bf{Hence}}}}$

• Base = (x+2) = (6+2) = 8 unit .
• Perpendicular (x) = 6 unit

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