The sides of a right-angled triangle containing the right angle are 4x cm and (2x-1) cm. if the area of the triangle is 30cm^2; Calculate the length of its sides
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Step-by-step explanation:
area ⇒30 cm
2
=
2
1
(2x−1)(4x)
60=(4x)(2x−1)
15=x(2x−1)
2x
2
−x−15=0
2x
2
−6x+5x−15=0
2x(x−3)+5(x−3)=0
⇒x=3,x=
2
−5
since x cannot be negative
x=3
∴AB=(2x−1)=5 cm
AC=4x=12 cm
BC=
AB
2
+AC
2
=
25+144
+
169
=13cm.
∴ the sides are 5 cm, 12 cm and 13 cm
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