Question

The hypotenuse of a right-angled triangle is 25cm and the two legs are in the ratio of 3:4. Find the legs.

Answer 1

Given,

The hypotenuse of a right angled triangle = 25 cm

Two legs are in ratio = 3:4

To find,

The length of the two legs.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Let, the length of two legs = 3x cm and 4x cm

Here, we have to apply the Pythagoras theorem. (assuming that two legs are base and height of the triangle)

Now,

(3x)²+(4x)² = (25)²

Or, 9x²+16x² = (25)²

Or, 25x² = (25)²

Or, x² = (25)²/25

Or, x² = 25

Or, x = 5

(x can be ±5, but we have omitted the negative value, because length of something cannot be negative.)

So, the length of first leg = 3x = 3×5 = 15 cm

Length of second leg = 4x = 4×5 = 20 cm

Hence, the length of first leg is 15cm and length of second leg is 20cm.

Answer 2

Given,

The hypotenuse of right-angles triangle is $25cm$ and two legs are in the ratio of $3:4$.

Here, we are using Pythagoras theorem to find the sides

Let, the two legs be $3x$ and $4x$

Pythagoras theorem

$Hypotenuse^{2}=base^{2}+height^{2}$

Here, Hypotenuse $= 25$

Substitute given values, we get

$25^{2} =(3x)^{2}+(4x)^{2}$

$625=9x^{2} +16x^{2}$

$625=25x^{2}$

$x^{2} =\frac{625}{25}$

$x^{2} =25$

$x=5$

Substitute $x=5$ in two legs

$3x=3\times5=15\\4x=4\times5=20$

Therefore, the legs are$15$ and $20$.