Find the value of x.
Answers
In triangle ADC
h² = p²+b²
17² = 8² + b²
289 = 64 + b²
289 - 64 = b²
225 = b²
15 = b²
BC - DC = BD
21 - 15 = BD
6 = BD
In triangle ABD
h² = p² + b²
h² = 8² + 6²
h² = 64 + 36
h² = 100
h = 10
.
. . The value of x is 10 .
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x = 10 units
Step-by-step explanation:
GIVEN
AD = 8 units
AC = 17 units
BC = 21 units
___________________________
TO FIND
AB
___________________________
Let's find DC
We know that,
Hypotenuse² = Height² + Base²
Here,
Hypotenuse = AC = 17 units
Height = AD = 8 cm
We know that,
Hypotenuse² = Height² + Base²
Base² = Hypotenuse² - Height²
Base² = AC² - AD²
Base² = 17² - 8²
Base² = 289 - 64
Base² = 225
Base = √225
Base = 15
Base = 15 units
DC = 15 units
___________________________
Let's find BD
We know that,
BD + DC = 21
BD + 15 = 21
BD = 21 - 15
BD = 6
BD = 6 units
___________________________
Let's find AB
We know that,
Hypotenuse² = Height² + Base²
Here,
Hypotenuse = AB = x
Height = AD = 8 cm
Base = BD = 6 cm
We know that,
Hypotenuse² = Height² + Base²
Hypotenuse² = AD² + BD²
Hypotenuse² = 8² + 6²
Hypotenuse² = 64 + 36
Hypotenuse² = 100
Hypotenuse = √100
Hypotenuse = 10