Question

(10) The legs of a right triangle are in the ratio 3 : 4 and its area is 1014 cm. Find the lengths of its sides and its perimeter.​

Answer 1

Step-by-step explanation:

Let it's leg be 3x and 4x. Then,

according to question,

Area of right angle triangle = 1/2 × 3x × 4x

1,014 = 6x^2

1,014/6 = x^2

√169 = x

13 cm = x

Hence, first side = 3×13 = 39 cm

second side = 4×13 = 52 cm.

We know that

H^2 = P^2 + B^2

H^2 = 39^2 + 52^2

H^2 = 1521 + 2704

H = √4225

H = 65 cm.

Hence, the hypotenuse is 65 cm.

Perimeter of triangle = sum of all side

so,

perimeter = 39+52+65 cm

perimeter of triangle = 156 cm

Answer 2

Let the legs of the right triangle be 3x and 4x respectively

• 3x be the base of the right triangle
• 4x be the height of the right triangle

Then, area of the triangle = (1/2) × base × height

1014 = (1/2) × (3x) × (4x)

1014 = 0.5 × 12x2 1014

= 6x2 X2 = (1014/6) X2 = 169 X = √169 X = 13

∴The base of the right triangle 3x = 3 × 13 = 39 cm

The height of the right triangle 4x = 4 × 13 = 52 cm