Question

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

Answer 1

Let the other two sides be 4x and 3x because they're in the ratio 4:3.

As it is a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the perpendicular sides (i.e., 4x and 3x), according to Pythagoras' theorem.

So,

$\displaystyle \begin{aligned}(4x)^2+(3x)^2&=20^2 \\ \\ 16x^2+9x^2&=400 \\ \\ 25x^2&=400\\ \\ x^2&=\frac{400}{25}\\ \\ x^2&=16\\ \\ x&=4\end{aligned}$

Thus,

$\large \Longrightarrow\ 4x=4 \times 4=\ \textbf{16 cm} \\ \\ \\ \Longrightarrow\ 3x=3 \times 4 =\ \textbf{12 cm}$

Hence the lengths of the other sides are 16 cm and 12 cm.

Answer 2

Answer:

16cm and 12cm

Step-by-step explanation:

let the other sides be 4y and 3y

(P)²+ (B)² = (H)²

(4y)²+ (3y)² =(20)²

16y²+ 9y² = 400

y² = 400/25

= 16

y = √16 =4

4y = 4•4 = 16cm

3y = 3•4 = 12cm