Question

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Answer 1

Step-by-step explanation:

Given:

In triangle ABC

ABP = AC? + BC2

To find:

Whether triangle ABC is right angled or not

Solution:

Converse of Pythagoras theorem:

If square of one side of a triangle is equal to sum of the squares of the other two sides, then the angle contained

by the two sides is right angle.

Consider,

ABP = AC? + BC?

According to converse of Pythagoras theorem,

AABC is right angled

Triangle CAB is isosceles triangle with base AB=2 and AC=BC=7

Dropping a perpendicular from C on AB at E will bisect AB I.e EB=1

Also triangle CEB will be right angled triangle, with hypotenuse CB=7, base EB=1, and perpendicular can be calculated using Pythagoras

Perpendicular= rt(CB^2-EB^2)=rt48

Also triangle CED is right angled triangle where perpendicular CE=rt48, hypotenuse, CD=8 and base ED=x

Using Pythagoras find ED

ED=rt(8^2-48)=rt16=4

BD=ED-EB=4-1=3