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Sagot :

AD = 2x -4 = 2times 32 -4 = 60

the answer is 60, hope I helped u!

s1m1

Answer:

AD = 60

Step-by-step explanation:

→If DE ║ AB is given , then ∠E ≅∠B  and ∠D ≅ ∠A ( corresponding angles are congruent) there for ΔCDE ≈ ΔCAB ( because of the AA similarity theorem.)

→Since ΔCDE ≈ ΔCAB then their sides are in proportion so we write the proportions:

CD / CA = CE / CB

→substitute the sides with what is given in the picture, and find x so we can further find AD.

5x / 5x+2x-4 = 8x / 8x+3x, combine like terms

5x / 7x-4 = 8x / 11x, cross multiply

5x * 11x = 8x *(7x-4), multiply and distribute multiplication over subtraction

55x² = 56x² - 32x, subtract 56x² and add 32x to both sides of the equation

55x² - 56x² +32x = 0, combine like terms

-x² +32x = 0, factor -x

-x(x-32) = 0, so there are 2 possibly situation

→ Find x then substitute in AD = 2x-4 to find AD

-x = 0  so x = 0, will give us AD = 2x-4 = 2*0 -4 = -4, we reject this solution because a length can not be negative

x-32 = 0 so x= 32, will give us AD = 2x -4 = 2*32 -4 = 64 -4 = 60.

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