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uysha [10]
3 years ago
13

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

.
What is the length of LF?
Mathematics
1 answer:
weqwewe [10]3 years ago
4 0

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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