Question

In a right - angled triangle ,if the hypotensue is 20cm and the ratio of the other two sides is 4:3, find the sides.​

Answer 1

Answer :

• Sides are 16cm and 12cm

Given :

• In a right angled triangle, if the hypothenuse is 20cm and the ratio of the other two sides is 4 : 3

To find :

• Sides

Solution :

Given,

• Hypotenuse = 20cm
• Ratio of other two sides = 4 : 3

Then,

• Let the altitude be 4x
• Let the base be 3x

We know that,

• Pythagoras theorem = h² = b² + a²

Where,

• h is hypothenuse
• b is base
• a is altitude

According to Pythagoras theorem :

⇢ h² = b² + a²

⇢ (20)² = (3x)² + (4x)²

⇢ 400 = 9x² + 16 × 2

⇢ 400 = 25x²

⇢ 25x² = 400

⇢ x² = 400/25

⇢ x² = 16

⇢ x = 4

Now , To find the sides :

⇢ Altitude = 4x

⇢ 4(4)

⇢ 16cm

⇢ Base = 3x

⇢ 3(4)

⇢ 12cm

Hence , Sides are 16cm and 12cm.

Answer 2

Answer:

According to Pythagoras theorem :-

→

${h}^{2} = {b}^{2} + {a}^{2}$

→

$( {20})^{2} = ( {3x})^{2} + (4x )^{2} \\ 400 = {9x}^{2} + 16 \times 2 \\ 400 = {25x}^{2} \\ {25x}^{2} = 400 \\ {x}^{2} = \frac{400}{25} \\ {x}^{2} = 16 \\ x = 4$

Now , the Sides :-

→

$a = 4 x \\ 4(14) \\ 16cm \\ \\ b = 3x \\ 3(4) \\ 12cm$