Question

In fig. the correct relation between x, a, b and c is:
a. x²- a²=b²- c²
b. x²+ a²=b²+ c²
c. x²=a²+ c²- b²
d. x=2a-b+c​

Answer 1

Answer:

c. x²=a²+c²-b²

Step-by-step explanation:

In ∆ ADC

by using Pythagoras theorem we get,

a²+c²=AC² (say i)

and In ∆ABC

b²+x²=AC² (say ii)

from (i) and (ii) we get

a²+c²=b²+x²

a²+c²-b²=x²

Answer 2

Given:

A figure having two right-angled triangles ABC and ADC.

AB= b units, BC= x units, CD= c units and AD= a units.

To find:

Relationship between x, a, b and c.

Solution:

According to Pythagoras theorem, in a triangle ABC, if angle B= 90°, BC is a base, AB is the height of the triangle, then AC will be hypotenuse which is determined by using the formula:

$AC = \sqrt{ {AB}^{2} + {BC}^{2} }$

So,

Applying Pythagoras theorem in right-angled triangle ABC we have,

$AC = \sqrt{ {b}^{2} + {x}^{2} } \: \: \:(i)$

Similarly, in a right-angled triangle ADC we have,

$AC = \sqrt{ {a}^{2} + {c}^{2} } \: \: \: \: (ii)$

So, equating (i) and (ii) we have

x²+ b² =a²+ c²

Hence, x²=a²+ c²- b²

So, the correct option is c. x²=a²+ c²- b².