Question

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

Answer 1

Answer:

$a = 30$

$b = 40$

Step-by-step 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

$\frac{a}{40} = \frac{a+15}{60}$

Multiply both sides by (60)(40)

$(60)*(40)*\frac{a}{40} = (60)*(40)*\frac{a+15}{60}$

$60a = 40(a+15)$

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

$\frac{20a}{20} = \frac{600}{20}$

$a = \frac{600}{20}$

$a = 30$

Similarly;

$\frac{b}{40} = \frac{b+20}{60}$

Multiply both sides by (60)(40)

$(60)*(40)*\frac{b}{40} = (60)*(40)*\frac{b+20}{60}$

$60b = 40(b+20)$

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

$\frac{20b}{20} = \frac{800}{20}$

$b = \frac{800}{20}$

$b = 40$