Question

find the lengths of its legs​

Answer 1

Answer:

Breadth = 30cm

Height = 40cm

Step-by-step explanation:

Legs = 3:4

Breadth = 3x

Height = 4x

Area of triangle = 1/2 bh = 1/2 (3x * 4x) = 1/2 * 12x²

1/2 * 12x² = 6x²

6x² = 600cm²

6x²/6 = 600/6

x² = 100

x = √100

x = 10

Length of legs -

Breadth = 3x = 3 x 10 = 30cm

Height = 4x = 4 x 10 = 40cm

Answer 2

Answer:

30cm & 40cm

Step-by-step explanation:

Let common multiple be y.

therefore 3:4= 3y and 4y

now,

in the triangle,

Area=600 square cm

Area(of right triangle)=1/2 x leg1 x leg2

therefore area=1/2 x 3y x 4y

                       =1/2 x 12(y^2)

                       =6(y^2)

600 square cm=6(y^2)

therefore, y= √(600/6)

y=√100

y=10

therefore leg1=3y=3 x 10=30cm

leg2=4y=4 x 10=40cm