Question

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Answer 1

Information given to us:

• Hypotenuse of a right angled triangle is of 26cm
• Sum of other two sides of that triangle is 34cm

Need to be calculated by us:

• We have to find the length of its sides?

Let us assume:

• Length of its second side be y cm
• Length of its third side be (34-y) cm

Usage of concept:

• Pythagoras Theorem

Pythagoras theorem gives us knowledge about how to came to know the sides of triangle by simply knowing it's hypotenuse.

It's formula is,

• (Hypotenuse)² = (base)² + (Perpendicular)²

Or,

• BC² = AB² + AC²

Substituting the required values:

(26)² = y² + (34 - y)²

On squaring 26 we gets,

676 = y² + (34 - y)²

On squaring (34 - y)² we gets,

676 = y² + 1156 - 68y + y²

Now,

676 = 2y² + 1156 - 68y

Reversing the sides,

2y² + 1156 - 676 - 68y = 0

On subtracting 1156 with 676 we gets,

2y² + 480 - 68y = 0

Dividing each term from 2,

y² + 240 - 34y = 0

It can be rewritten as,

y² - 34y + 240 = 0

Splitting middle term,

y² - 10y - 24y + 240 = 0

Grouping terms,

y(y - 10) - 24(y - 10)

(y - 24) (y- 10)

We gets,

y as 24 and 10

Finding out length of its sides:

Given,

• Length of its second side is y cm

So, y is 10cm

• Length of its third side is (34-y) cm

So, (34 - 10) = 24cm

• Length of first side is 26 cm

It is already given in question.