Question

4 The hypotenuse of a right-angled triangle is 25 cm. The other two sides are such that one is 5 cm longer
than the other. Their lengths in centimetres are​

Answer 1

Step-by-step explanation:

Answer:-

Refer to Attachment if any confusion regarding diagram.

Concept:-

To apply Pythagoras Theroem

Let's Do!

$\boxed{\sf{(Hypotenuse)^2= (Base)^2 + (Height)^2}}$

• This is the Pythagoras Theorem.

$\sf{(Hyp)^2= (Base)^2 + (Height)^2}$

• Height is x
• Base is x+5
• Hypotenuse is 25.

$\sf{(25)^2= (x+5)^2 + (x)^2}$

$\sf{625= x^2+5^2+ 10x + x^2}$

$\sf{625= x^2+ 25 + 10x + x^2}$

$\sf{625= 2x^2+ 25 + 10x }$

$\sf{625-25= 2x^2+ 10x }$

$\sf{600= 2x^2+ 10x }$

Factorisation:-

$\sf{0= 2x^2+ 10x -600 }$

$\sf{0= 2x^2+ 40x - 30x -600 }$

$\sf{0= 2x^2+ 40x - 30x -600 }$

$\sf{0= 2x(x+ 20) - 30(x + 20)}$

$\sf{0= (2x-30)(x+ 20)}$

Ignoring Negative Value,

$\sf{0= (2x-30)}$

$\sf{30= 2x }$

$\sf{x= 15 \ cm}$

And, Base will be $\sf{x+5= 20\ cm}$

Answer 2

$\huge \sf \: GIVEN$

• The hypotenuse of a right-angled triangle is 25

$\huge \sf \: TO \: FIND$

• The other two sides

$\huge\sf \: SOLUTION$

Given: Hypotenuse of right triangle =25 cm

Let the other sides be x and x+5

By applying Pythagoras Theorem:

$25 {}^{2} =x {}^{2} +(x+5) {}^{2} \\ </p><p>625=x{}^{2}+x{}^{2}+25+10x \\ </p><p>2x {}^{2} +10x−600=0 \\ </p><p>x {}^{2} +5x−300=0 \\ </p><p>x {}^{2} +20x−15x−300=0 \\ </p><p>(x+20)(x−15)=0 \\ </p><p> \pink{ \sf \: x=15,20}</p><p></p><p>$

So, the other two sides are 15 cm and base is 20 cm.