Question

The sides of triangle are in the ratio 7 : 8 : 9 then
(A) angles of the triangle are in the ratio 7 : 8 : 9 (B) it is an acute angled triangle
(C) it is a right angled triangle (D) it is an obtuse angled triangle

Answer 1

Step-by-step explanation:

let ratio be the x

as we know the measurement of the angle is 180 degree

24x = 180°

x = 180/24

= 80° ieach

7x +8x +9x = 180°

. as it is less than 90 degree it means it is an acute angle

Answer 2

Given :-

The sides of triangle are in the ratio 7 : 8 : 9 then

To Find :-

Which option is correct

Solution :-

Option A is incorrect because sides and angles are different things. The ratio of sides is 7:8:9 not of the angles.By using Pythagoras theorem

Rules for a triangle :

If the sum of the square of base and height is greater than hypotenuse then it is an acute-angled triangle.

a² + b² > c²

If the sum of the square of base and height is equal to hypotenuse then it is a right-angled triangle.

a² + b² = c²

If the sum of the square of base and height is less than hypotenuse then it is an obtuse-angled triangle.

a² + b² < c²

Now, checking each option by the properties

Let the sides be 7x, 8x and 9x

(7x)² + (8x)² = (9x)²

49x² + 64x² = 81x²

113x² > 81x²

As

a² + b² > c². Hence, it's an acute-angled triangle. Option B is correct