Question

Can someone please help? Thank you :)

Answer 1

The value of x is 8.

Solution:

Given $\triangle V D G \sim \triangle V N Q$.

DG = 60, NQ = 48, DN = 15, NV = x + 4

To find the value of x:

Property of similar triangle:

If two triangles are similar then the corresponding angles are congruent and the corresponding sides are in proportion.

$\Rightarrow\frac{DG}{NQ} =\frac{DN}{NV}$

$\Rightarrow\frac{60}{48} =\frac{15}{x+4}$

Do cross multiplication.

$\Rightarrow60(x+4)=15\times48$

$\Rightarrow60x+240=720$

Subtract 240 from both side of the equation.

$\Rightarrow60x+240-240=720-240$

$\Rightarrow60x=480$

Divide by 60 on both sides of the equation.

$\Rightarrow\frac{60x}{60} =\frac{480}{60}$

$\Rightarrow x=8$

Hence the value of x is 8.