Question

in ∆ABC, AB = BC, AC = 7√2 find value of x​

Answer 1

Answer:

Given:-

BC=AC

then

angle BAC=BCA(if two opposite sides of a triangle are equal then their opposite angles are also equal)

that is

BAC=45°

Also

BAC+BCA+ABC=180°(sum of all interior angles of a triangle are supplementary)

45+45+ABC=180

ABC=180-90

ABC=90°

therefore ABC is a right angle

and AC is it's opposite side

that is AC is the Hypotenuse

For knowing Hypotenuse

we use Pythagoras Theorem

that is

Hypotenuse²=base²+altitude²

here

Hypotenuse²=7√2

also base=altitude (AC=BC)

Let them be x

therefore

7√2=√(x²+x²)

7√2=√2x²

√2x²=7√2

2x²=(7√2)²

2x²=49×2=98

x²=98/2=49

x=√49

x=7

therefore the base and altitude are 7 cm each

Let's check whether it's correct or not

by using Pythagoras theorem

that is

Hypotenuse²=base²+altitude²

Hypotenuse²=7²+7²=49+49=98

Hypotenuse=√98 (√7×7×2)

Hypotenuse=7√2

hence verified

hope it helps