Question

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

Answer 1

Step-by-step explanation:

Given :-

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

It's area is 1014 cm².

To find :-

Lengths of the legs of the right triangle.

Solution :-

Given that

The ratio of the legs of a right triangle = 3:4

Let they be 3X cm and 4X cm

Let a = 3X cm

Let b = 4X cm

We know that

Area of a right angled triangle whose legs a units and b units is (1/2)ab sq.units

Therefore, Area of the right triangle

=> A = (1/2)×3X × 4X cm²

=> A = 12X²/2 cm²

=> A = 6X² cm²

According to the given problem

Area of the right triangle = 1014 cm²

=> 6X² = 1014

=> X² = 1014/6

=> X² = 169

=> X = ±√169

=> X = ±13

Since , X is a length , X can't be negative

Therefore, X = 13 cm

Now,

If X = 13 cm then 3X = 3(13) = 39 cm

If X = 13 cm then 4X = 4(13) = 52 cm

Answer:-

The legs of the right angled triangle are 39 cm and 52 cm respectively.

Used formulae:-

→ Area of a right angled triangle whose legs a units and b units is (1/2)ab sq.units

Answer 2

GIVEN :

• The legs of a right triangle are in the ratio and its area is 1014 cm2.

To Find :

• find the lengths of other legs.

SOLUTION :

In a right-angled triangle, if one leg is the base, then the other leg is the height.

Let the given legs be 3 x and 4x respectively then -:

area of the traingle = (1/2 × 3x × 4x)

area of the traingle = (6x) cm

Understand that, it is given that area of the triangle is 1410 cm2 in the question. Therefore,

1014 = 6x²

x² = (1014/6)

Solve further,

x² = 169

x = √169

x = 13

Calculate the lengths of the other legs.

Base = ( 3 × 13)

= 39

Height = (4 × 13)

= 52 cm

Hence, the lengths of the other legs are 39 cm and 52 cm.