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Aneli [31]
2 years ago
12

ADHE - ADGF below. Find the value of 'x'. X H н E 8 2. 12

Mathematics
1 answer:
Vlad1618 [11]2 years ago
8 0

Given:

\Delta DHE\sim \Delta DGF

To find:

The value of x.

Solution:

We know that, corresponding sides of similar triangles are proportional.

Since,\Delta DHE\sim \Delta DGF, therefore

\dfrac{HE}{GF}=\dfrac{DE}{DF}

On substituting the values from the figure, we get

\dfrac{8}{12}=\dfrac{x}{x+2}

\dfrac{2}{3}=\dfrac{x}{x+2}

On cross multiplication, we get

2(x+2)=3x

2x+4=3x

4=3x-2x

4=x

Therefore, the value of x is 4.

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