Question

PLEASEEE HELP !! What is the value of x ?

Answer 1

Answer:

x = 20 cm

Step-by-step explanation:

The triangles given are similar triangles because they share the same angles.  Because they are similar, their side lengths are in the same ratio, or proportion to one another.  The left side of the larger triangle has a length of 121cm + 11cm = 132cm where the smaller triangle only has a length of 11 cm.  We can put these lengths into a ratio:

$\frac{larger}{smaller}=\frac{132}{11}=\frac{12}{1}$

Since the other side of the triangle would have to be in the same proportion, or ratio, we can set up the following proportion:

$\frac{12}{1}=\frac{(5x+10)+10}{10}=\frac{5x+20}{10}$

Use cross-multiplication: 5x + 20 = (10)(12) or 5x + 20 = 120

Subtract 20 from each side: 5x + 20 - 20 = 120 - 20 or 5x = 100

Divide and solve for 'x':  5x/5 = 100/5 or x = 20 cm