Question

In a right angled triangle ,if hypotenuse is 20 cm and the ratio of others two sides is 4:3,find the sides​

Answer 1

Given ,

Hypotenuse of Δ = 20 cm

The ratio of other two sides is 4 : 3

Let , the measure of other two sides are 4x and 3x

We know that , In right angled triangle

$\boxed{ \tt{(h)}^{2} = {(b)}^{2} + {(p)}^{2} }$

Thus ,

(20)² = (3x)² + (4x)²

400 = 9(x)² + 16(x)²

400 = 25(x)²

(x)² = 400/25

(x)² = 16

x = ± 4 cm

Since , the length can't be negative

Hence , the measure of other two sides are 16 cm and 12 cm

Answer 2

✬ Sides = 16 & 12 cm ✬

Step-by-step explanation:

Given:

• Measure of hypotenuse is 20 cm.
• Ratio of two sides is 4 : 3.

To Find:

• What is the measure of sides ?

Solution: Let x be the common in given ratios. Therefore,

➟ Sides are 4x and 3x

Let in right angled triangle at ABC, we have

• Hypotenuse = 20 cm
• Perpendicular = 4x cm
• Base = 3x cm

Pythagoras Theorem :- In a right angled triangle the square on the hypotenuse is equal in area to the sum of the squares on the other two sides.

★ H² = P² + B² ★

$\implies{\rm }$ 4x² + 3x² = 20²

$\implies{\rm }$ 16x² + 9x² = 400

$\implies{\rm }$ 25x² = 400

$\implies{\rm }$ x² = 400/25

$\implies{\rm }$ x² = 16

$\implies{\rm }$ x = √16

$\implies{\rm }$ x = 4

So, the sides are

➬ Hypotenuse is 20 cm

➬ Perpendicular is 4(4) = 16 cm

➬ Base is 3(4) = 12 cm

__________________

★ Verification ★

➯ 20² = 16² + 12²

➯ 400 = 256 + 144

➯ 400 = 400

$\large\boxed{\texttt{Verified}}$