The hypotenuse of a right-angled triangle is 3V5cm.if the larger side is twice the smaller side. Find the length of the larger side.
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Answer:
Let the smaller side of the right triangle be x cm and the larger side by y cm.
Then, x
2
+y
2
=(3
5
)
2
⇒x
2
+y
2
=45....(i)
If the smaller side is tripled and the larger side be doubled, the new hypotenuse is 15cm.
∴(3x)
2
+(2y)
2
=15
2
⇒9x
2
+4y
2
=225...(ii)
From equation (i) we get y
2
=45−x
2
Putting y
2
=45−x
2
in equation (ii), we get
9x
2
+4(45−x
2
)=225⇒5x
2
+180=225⇒5x
2
=45⇒x
2
=9⇒x=±3
But length of a side cannot be negative. Therefore x=3
Putting x=3 in (i) we get
9+y
2
=45⇒y
2
=36⇒y=6
Hence, the length of the smaller side is 3cm and the length of the larger side is 6cm.
Step-by-step explanation:
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