Question

The hypotenuse of a right-angled triangle
is 25 m long. The difference between the
length of other two sides is 5 metres. Find
the length of other sides of the triangle.​

Answer 1

Answer:

Let one of the side be x and the other be x+5

By Pythagoras theorem,

(25) ²=x²+(x+5) ²

625=x²+x²+10x+25

625=2x²+10x+25

2x²+10x-600=0

x²+5x-300=0

x²+20x−15x−300=0

x(x+20)−15(x+20)=0

(x+20)(x−15)=0

x+20=0 and x−15=0

∴ x=−20 and x=15

But x cannot be negative.

Hence, one side =x=15cm

⇒ Other side x+5=15+5=20cm

Step-by-step explanation:

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Answer 2

Given :-

• The hypotenuse of a right-angled triangle
• is 25 m long. The difference between the
• length of other two sides is 5 metres.

To Find :-

• The Length of the other sides of traingle = ?

Answer :-

• The Length of the other sides of traingle = 15 m and 20 m.

Explaination :-

Let x be the one of the side then the other side is x - 5.

★ According to Question :-

• By Phythagoras theorem we get :

→ (Hypotenuse)² = (Base)² + (Perpendicular)²

→ (25)² = (x)² + (x + 5)²

→ 625 = x² + x² + 25 + 10x

→ 625 = 2x² + 10x + 25

→ 2x² + 10x + 25 - 625 = 0

→ 2x ² + 10x - 600 = 0

• Dividing the whole term by 2 we get :

→ x² + 5x - 300 = 0

→ x² - 15x + 20x - 300

→ x(x - 15) + 20(x - 15)

→ (x + 20) (x - 15)

→ x = -20 or x = 15

• As we know that, Length of side cant be negative. So, x = 15

→ x = 15 m

Hence,

• Length of one side = x = 15 m
• Length of other side = x + 5 = 15 + 5 = 20 m