Question

In triangle ABC,angle B =90°,AC = √208 cm. Area of the triangle is 48 square centimetre. then find the following ,x^2 + y^2?​

Answer 1

Answer:

208

Step-by-step explanation:

Let

AB = x

BC = y

B is a 90 degree angle

so its a right angle triangle

By Pythagoras theorem

x^2 + y^2 = AC^2

AC = √208 GIVEN

x^2 + y^2 = 208

Answer 2

CORRECT QUESTION

ABC is a right angled triangle with base BC.Angle B =90,AC= √208 cm,AB= X cm,BC= Y cm & area of the triangle is equal to 48sq.cm.Then

a) what is the value of X² + Y² ?

b)what is the value of XY ? (hint area=1/2bh)

ANSWER

(a) The value of X²+ Y² = 208cm

(b) The value of XY = 96cm.

GIVEN

ABC is a right angled triangle with base BC.Angle B =90,AC= √208 cm,AB= X cm,BC= Y cm & area of the triangle is equal to 48sq.cm

TO FIND

(a) the value of X² + Y²

b) the value of XY

SOLUTION

We can simply solve the above problem as follows;

It is given,

Area of triangle = 48cm²

AC = X

BC =Y

We know that,

Area of a right angle triangle =

$\frac{1}{2} \times base \times height$

Where,

Base = Ycm

Height = X cm

Putting the values in the above formula we get,

$48 = \frac{1}{2} \times \: XY$

XY = 2 × 48 = 96cm

Now,

Applying Pythagorus theorem in ΔABC

AC² = AB² + AC²

Putting the values in the above formula we get,

$( \sqrt{280} )^{2} = X^{2} + {Y}^{2}$

X² + Y² = 208

Hence, The value of X²+ Y² = 208cm and the value of XY = 96cm.

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