Question

The legs of a right triangle are in the ratio 3:4 and its area is 1014 cm². Find the lengths of its legs

Answer 1

let the legs be 3x and 4x

area = (12x*2)/2
= 6x*2

6x*2 = 1014
x*2 = 169
x = 13

legs are of length 39 and 52

Answer 2

Answer:

39 cm and 52 cm.

Step-by-step explanation:

We are give that The legs of a right triangle are in the ratio 3:4

let the ratio be x

So, the legs of a right triangle are 3x and 4 x

Area of triangle = $\frac{1}{2} \times base  \times Height$

                          = $\frac{1}{2} \times 3x  \times 4x$

                          = $6x^2$                    

Since we are given that its area is 1014 cm².

So,  $1014 = 6x^2$        

$\frac{1014}{6}=x^2$        

$169=x^2$        

$13=x$        

So, $3x = 3 \times 13 = 39 cm$

$4x = 4 \times 13 = 52 cm$

Thus the legs of the right triangle is 39 cm and 52 cm.