Question

In the figure below, the segment is parallel to one side of the triangle. Find the value of x.

Answer 1

Answer: x= .$18\frac{2}{3}$.

Step-by-step explanation: We are given a segment parallel to the base.

Therefore, sides of big triangle and small triangles would be in proportion.

$\frac{One \ Side \ of\ big \ triangle }{One \ Side \ of\ small \ triangle} =\frac{Other \ Side \ of\ big \ triangle }{Other \ Side \ of\ small \ triangle}$

Setting values for the shown triangle, we get

$\frac{x+(x+7)}{x} =\frac{16+22}{22}$

$\frac{2x+7}{x} =\frac{38}{16}$

On cross multiplication, we get

16(2x+7) = 38(x)

32x + 112 = 38x.

Subtracting 112 from both sides, we get

32x + 112-112 = 38x -112

32x = 38x-112

Subtracting 38x from both sides, we get

32x-38x = 38x-38x-112

-6x = -112

Dividing both sides by -6, we get

$\frac{-6x}{-6} =\frac{-112}{-6}$

x= .$18\frac{2}{3}$.

Therefore, x= .$18\frac{2}{3}$.