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14 Jun 2020, 09:26
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Hi all,
In ∆ABC, angle ABC is a right angle (90°) making ∆ABC a right angle triangle. By usuing hypotenuse theorem, we can get our first equation:
a²+b²=324 ------ (1)
We are given that BD is perpendicular to AC making angles BDC and BDA right angles. By usuing hypotenuse theorem in ∆BDC we get,
BD=√a²-100 ------(2)
By usuing hypotenuse theorem in ∆BDA we get,
BD= √b²-64 ------(3)
From eqations (2) and (3) we get,
√a²-100=√b²-64
=> a²-100=b²-64 (removing the underoot by squaring sides)
=> a²-b²=36------(4)
Solving equations (1) and (4) by addition we get,
a²+b²=324
a²-b²= 36
__________
2a² =360
=> a²=180
Putting value of a² in equation (1) we get,
180+b²=324
=>b²=324-180
=>b²=144
=>b=√144
=>b=+12 or -12
=>b=12 (measurements can not be negative)
This option (B) i.e 12 is the answer
(Detailed step by step solution)
Hope this helped!
Posted from my mobile device
In ∆ABC, angle ABC is a right angle (90°) making ∆ABC a right angle triangle. By usuing hypotenuse theorem, we can get our first equation:
a²+b²=324 ------ (1)
We are given that BD is perpendicular to AC making angles BDC and BDA right angles. By usuing hypotenuse theorem in ∆BDC we get,
BD=√a²-100 ------(2)
By usuing hypotenuse theorem in ∆BDA we get,
BD= √b²-64 ------(3)
From eqations (2) and (3) we get,
√a²-100=√b²-64
=> a²-100=b²-64 (removing the underoot by squaring sides)
=> a²-b²=36------(4)
Solving equations (1) and (4) by addition we get,
a²+b²=324
a²-b²= 36
__________
2a² =360
=> a²=180
Putting value of a² in equation (1) we get,
180+b²=324
=>b²=324-180
=>b²=144
=>b=√144
=>b=+12 or -12
=>b=12 (measurements can not be negative)
This option (B) i.e 12 is the answer
(Detailed step by step solution)
Hope this helped!
Posted from my mobile device
14 Jun 2020, 09:46
Kudos
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C is the answer.
You can check using Pythagorus.
18^2= 324
C^2= 180
So 324-180= 144. Which is a perfect square. So c is the answer.
Posted from my mobile device
You can check using Pythagorus.
18^2= 324
C^2= 180
So 324-180= 144. Which is a perfect square. So c is the answer.
Posted from my mobile device
14 Jun 2020, 12:52
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Using Pythagoras theorem
In triangle ABD & CBD,
b^2 = x^2 + 64
a^2 = x^2 + 100
In triangle ABC
a^2 + b^2 = 324
2x^2 = 324 - 164
x^2 = 80
b^2 = 80 + 64 = 144
b = 12
Posted from my mobile device
In triangle ABD & CBD,
b^2 = x^2 + 64
a^2 = x^2 + 100
In triangle ABC
a^2 + b^2 = 324
2x^2 = 324 - 164
x^2 = 80
b^2 = 80 + 64 = 144
b = 12
Posted from my mobile device
