Question

If K parallel to L find the value of a and the value of b.

Answer 1

`a = 30`

`b = 40`

Explanation:

Given

The attached triangle

Such that K is parallel to L

Required

Find the value of a and b

From the properties of parallel triangles;

Provided that k is parallel to l, then

`(a)/(40) = (a+15)/(60)`

Multiply both sides by (60)(40)

`(60)*(40)*(a)/(40) = (60)*(40)*(a+15)/(60)`

`60a = 40(a+15)`

Open Bracket

`60a = 40*a+40*15`

`60a = 40a+600`

Subtract 40a from both sides

`60a - 40a = 40a - 40a + 600`

`20a = 600`

Divide both sides by 20

`(20a)/(20) = (600)/(20)`

`a = (600)/(20)`

`a = 30`

Similarly;

`(b)/(40) = (b+20)/(60)`

Multiply both sides by (60)(40)

`(60)*(40)*(b)/(40) = (60)*(40)*(b+20)/(60)`

`60b = 40(b+20)`

Open Bracket

`60b = 40*b+40*20`

`60b = 40b+800`

Subtract 40b from both sides

`60b - 40b= 40b - 40b + 800`

`20b= 800`

Divide both sides by 20

`(20b)/(20) = (800)/(20)`

`b = (800)/(20)`

`b = 40`