Question

The sides of Triangle ABC measure 10. 12. and 15 centimeters. The sides of Triangle DEF measure 12. 16, and 20 inchesWhich statement about the triangles is true?A Triangle DEF is a right triangles triangle ABC is not a right triangleB Triangle ABC is a right triangle: triangle DEF is not a right triangle© Triangle ABC and Triangle DEF are both right triangles,D Neither Triangle ABC nor Triangle DEF is a right triangle.

Answer 1

Triangle DEF is a right triangle and triangle ABC is not a right triangle. ( option A)

Pythagoras theorem Can be used to find out if a triangle is right triangle.

Mathematically, Pythagoras states that;

c² = a² + b²

Where c is the longest in sides and a and b are the other 2 legs.

For triangle ABC

15² = 225

10² + 12² = 244

therefore triangle ABC is not a right triangle

For triangle DEF

20² = 400

16² + 12² = 400

therefore triangle DEF is a right triangle.

Therefore, the true statement is triangle DEF is a right triangle and triangle ABC is not a right triangle.

Answer 2

Given

The sides of the triangle ABC as 10cm, 12cm, 15cm.

The sides of the triangle DEF as 12inch, 16inch, 20inch.

To find which of the given statement is true.

Now,

By Pythagoras theorem, in a right angle triangle ABC,

`AB^2+BC^2=AC^2`

Therefore, for AB=10cm, BC=12cm, AC=15cm,

`\begin{gathered} 10^2+12^2=100+144 \\ =244 \\ \\e15^2(\because15^2=225) \end{gathered}`

Hence, triangle ABC is not a right triangle.

Also, for DE=12inch, EF=16 inch, DF=20 inch,

`\begin{gathered} DE^2+EF^2=12^2+16^2 \\ =144+256 \\ =400 \\ =20^2 \\ =DF^2 \end{gathered}`

Hence, triangle DEF is a right triangle.

Thus, option A is the correct answer.