Answer:
[tex]HG = 5[/tex]
Step-by-step explanation:
Given
[tex]HE = 8mm[/tex]
[tex]EF = 12mm[/tex]
[tex]Area = 68mm^2[/tex]
Find the length of HG
First, it should be noted that the displayed figure is a trapezium
The area of a trapezium is calculated by multiplying the sum of parallel sides by half its height;
In this case;
[tex]Area = \frac{HG + EF}{2} * HE[/tex]
Substitute the values of Area, HE and EF
[tex]68 = \frac{HG + 12}{2} * 8[/tex]
[tex]68 = (HG + 12) * 4[/tex]
Divide both sides by 4
[tex]\frac{68}{4} = \frac{(HG + 12) * 4}{4}[/tex]
[tex]17 = HG + 12[/tex]
Subtract 12 from both sides
[tex]17 - 12 = HG + 12 - 12[/tex]
[tex]5 = HG[/tex]
[tex]HG = 5[/tex]
Hence, the length of HG is 5mm
