Question

Triangle ABC has the side lengths 6 in., 9 in., and 11 in.

Which statement BEST describes how the triangle could be altered in order to make it a right triangle?
A
The 6 in. leg could be increased by a half-inch to make triangle ABC a right triangle.

B
One inch could be removed from the 9 in. leg and a new hypotenuse could be drawn.

C
The hypotenuse could be decreased to 10.8 in. to make triangle ABC a right triangle.

D
No change is necessary because the original triangle is a right triangle according to the converse of the Pythagorean Theorem.

Answer 1

Explanation:

B.

One inch could be removed from the 9 in. leg and a new hypotenuse could be drawn.

Answer 2

The BEST statement describes how the triangle could be altered in order to make it a right triangle

B.

One inch could be removed from the 9 in. leg and a new hypotenuse could be drawn.

Explanation:

Triangle ABC has the side lengths 6 in., 9 in., and 11 in.

The only condition is that satisfy to become Δ ABC a Right angle triangle is

Longer leg (one inch remove) = 9 - 1 = 8 inch

New hypotenuse = 10 inch

So that Pythagoras theorem must satisfy

`(\textrm{Hypotenuse})^(2) = (\textrm{Shorter leg})^(2)+(\textrm{Longer leg})^(2)`

So (Hypotenuse)² = 10² = 100

(Shorter leg)² = 6² = 36

(Longer leg)² = 8² = 64

So we have,

(Shorter leg)² + (Longer leg)² = 36 + 64

= 100

= (Hypotenuse)²

Therefore, Δ ABC is right Triangle By Converse of Pythagoras Theorem.

Therefore,

The BEST statement describes how the triangle could be altered in order to make it a right triangle

B.

One inch could be removed from the 9 in. leg and a new hypotenuse could be drawn.