In the diagram below, LATE is an isosceles trapezoid with LE ≅ AT , LA = 24, ET = 40, and AT = 10. Altitudes LF and AG are drawn
1 answer:
Answer:
6
Step-by-step explanation:
From the Trapezoid attached :
EF = GT
FG = LA
LE = AT = 10
LA = 24 ; FG = 24
FG + EF + GT = 40
Let : EF and GT = x
FG + 2x = 40
24 + 2x = 40
2x = 40 - 24
2x = 16
x = 16 ÷ 2 = 8
Hence, EF = GT = 8
Using Pythagoras :
Opposite² = hypotenus² - Adjacent²
LF² = LE² - FE²
LF² = 10² - 8²
LF² = 100 - 64
LF² = 36
LF = √36
LF = 6
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Answer:
CU = 117
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
=
substituting in values to the ratios
=
( cross- multiply )
24(36x - 1) = 3432 ( divide both sides by 24 )
36x - 1 = 143 ( add 1 to both sides )
36x = 144 ( divide both sides by 36 )
x = 4
CU = 36x - 1 - 26 = (36 × 4) - 27 = 144 - 27 = 117