What is the value of y in the diagram below
A.7 square root 2
B.2 square root 3
C.square root 14
D.square root 5
m∠ABD = m∠CBA because they are the same angle
m∠BDA = m∠BAC because they are both right angles.
So by the AA similarity theorem, triangle ABD is similar to triangle CBA
Do you see what to do next?
no i thought i did but then i got square root of 10 so no i don't get it still
sorry can you explain it further plz
Let's just look at the similarity statement △ABD ~ △CBA
△ABD ~ △CBA AB in the first triangle corresponds to CB in the second triangle.
△ABD ~ △CBA BD in the first triangle corresponds to BA in the second triangle.
AB / CB = BD / BA
Do you see where that came from?
All that's left to do is plug in the lengths of those sides and solve for y .
(5 +2) / y = y/2
7 / y = y / 2 cross myltiply
y^2 = 14
y = sqrt(14)