Question

The two triangles are similar.

What is the value of x?
Enter your answer in the box.
X=

Answer 1

Ratio remains same

`\\ \tt\Rrightarrow (3+12)/(4x)=(12)/(3x+1)`

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

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

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

`\\ \tt\Rrightarrow 3x=15`

`\\ \tt\Rrightarrow x=5`

Answer 2

x = 5

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:

⇒
`(3x+1)/(12)=(4x)/(15)`

Cross multiply and solve for x:

⇒ 15(3x + 1) = 12 · 4x

⇒ 45x + 15 = 48x

⇒ 15 = 3x

⇒ x = 5