Question

The two triangles are similar.
What is the value of x?
Enter your answer in the box.
X=

Answer 1

Answer:

x = 5

Step-by-step explanation:

Looking at the ratios of height to base:

Smaller triangle   3x + 1 : 12

Larger triangle   4x : 3 + 12  =  4x : 15

Therefore as triangles are similar:

3x + 1 : 12  =  4x : 15

Write as fractions:

⇒ $\dfrac{3x+1}{12}=\dfrac{4x}{15}$

Cross multiply and solve for x:

⇒ 15(3x + 1) = 12 · 4x

⇒ 45x + 15 = 48x

⇒ 15 = 3x

⇒ x = 5

Answer 2

Ratio remains same

$\\ \tt\Rrightarrow \dfrac{3+12}{4x}=\dfrac{12}{3x+1}$

$\\ \tt\Rrightarrow \dfrac{15}{4x}=\dfrac{12}{3x+1}$

$\\ \tt\Rrightarrow 15(3x+1)=12(4x)$

$\\ \tt\Rrightarrow 45x+15=48x$

$\\ \tt\Rrightarrow 3x=15$

$\\ \tt\Rrightarrow x=5$