Question

Triangle ABC has AB=4 and BC=7 then, (A) AC<7 (B) AC>4 (C) 4<AC<7 (D) 3<AC<11​

Answer 1

Answer:

(D) 3<AC<11.

Step-by-step explanation:

did something else is mention about triangle..?

if not then assume by yourself,

if ABC is right angled ,

there's a property that , |P + B| always > | H |

1. angle B is 90° then , AB + BC = 11 > AC

means AC < 11.

2. angle A is 90° then , AB + AC > BC

AC > 7 - 4= 3.

means AC > 3...

Answer 2

Concept: A triangle is a two-dimensional closed shape with three sides, three angles, and three vertices. A triangle is a polygon as well.

Given: AB = 4 cm, BC = 7 cm

To find: AC

Solution: According to the Triangle Inequality Theorem, the total of any two triangle sides must be bigger than the measure of the third side.

The measurement of sides of a triangle are 4 cm and 7 cm. Let us suppose the third side as $x.$

According to Pythagoras Theorem,

$Hypotenuse^{2} = Base^2 + Perpendicular^2\\H^2 = B^2 + P^2$

$7^2 = x^2 + 4^2\\49 = x^2 + 16\\49 - 16 = x^2\\36 = x^2\\6 = x$

Therefore, the third side AC of the triangle measures 6 cm.

Now, following the Triangle Inequality Theorem,

4 cm + 6 cm = 10 cm > 7 cm

4 cm + 7 cm = 11 cm > 6 cm

7 cm + 6 cm = 13 cm > 4 cm

So, from the options provided, the correct option is (D) 3 < AC < 11.

# SPJ2