Question

What is the value of x? enter your answer in the box. X = note: image not drawn to scale. Triangle g e h with segment e d such that d is on segment g h, between g and h. Angle g e d is congruent to angle d e h. E g equals 44. 8 millimeters, g d equals left parenthesis x plus 4 right parenthesis millimeters, d h equals 35 millimeters, and e h equals 56 millimeters.

Answer 1

Triangle GED and triangle DEH are similar triangles with a common side length DE

The value of x is 24

How to calculate the value of x

To calculate x, we make use of the following equivalent ratio

$GD : DH = EG : EH$

Substitute known values

$x + 4 : 35= 44.8 : 56$

Express the ratio as fraction

$\frac{x + 4}{35}= \frac{44.8}{ 56}$

Evaluate the quotient

$\frac{x + 4}{35}= 0.8$

Multiply both sides by 35

$x + 4= 28$

Subtract 4 from both sides

$x= 24$

Hence, the value of x is 24

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