Math, asked by imaanjavaid032, 5 months ago

By adding 5x + 2y, -7x + y, we get​

Answers

Answered by Lovelyfriend
1

ANSWER

Three sides of a triangle have been given. We find the intersection of these lines, taking two at a time to obtain the vertices and hence the area.

x+8y−22=0  ...(1)

5x+2y−34=0  ...(2)

2x−3y+13=0  ...(3)

Multiplying equation (2) by 4 and subtracting that from equation (1), we have

x+8y−22−(20x+8y−136)=0

⇒−19x+114=0

⇒x=6 and correspondingly y=2

Next, multiplying equation (2) by 3 and equation (3) by 2 and adding the two, we have

15x+6y−102+(4x−6y+26)=0

⇒19x−76=0 or x=4

⇒20+2y−34=0

⇒y=7

Third, multiplying equation (1) by 2 and subtracting equation (3) from this, we have

2x+16y−44−(2x−3y+13)=0

⇒2x+16y−44−2x+3y−13=0

⇒19y−57=0 or y=3

⇒2x−9+13=0 or x=−2

The three vertices thus become (6,2),(4,7),(−2,3)

The area of the triangle thus becomes 21×[6×7+4×3+(−2)×2−(2×4+7×(−2)+6×3)]

=21×[42+12−4−(8−14+18)]

=21×[50−12]

=19 sq unit

Similar questions