Given the perimeter of the triangle as $72$ , and two of the sides as $5 x$ and $4 x$ find the value of $x$ .

Open in App

Solution

Let the unknown side be $y$ .
Applying Pythagoras theorem gives us
$(5 x)^{2} = (4 x)^{2} + y^{2}$
$\Rightarrow 25 x^{2} - 16 x^{2} = y^{2}$
$\Rightarrow 9 x^{2} = y^{2}$
$\Rightarrow y = 3 x$
Therefore the perimeter of the triangle is $3 x + 5 x + 4 x = 12 x = 72$
$∴ x = \frac{72}{12} = 6$

Suggest Corrections

Similar questions

A B C

70

x, 4 x, 5 x

x

x^{2} - 5 x - 6 = 0

π / 3

(3 x^{2} - 5 x)

(4 x^{2} + 12)

(8 x^{2} - 9 x + 4)

The sides of a right angled triangle are 5x, 4x and 3x units respectively. If the perimeter is 36 units, what is x?

a, 2 a + 3

3 a - 3

60 c m

Join BYJU'S Learning Program