Question

A right-angled triangle has a base that is 7cm longer than its height, The hypotenuse of the
triangle is 23cm.
a) Show that h satisfies the equation h²+ah+b=0 State the value of a​

Answer 1

Step-by-step explanation:

AB

2

+BC

2

=AC

2

(By pythagoras theorem)

⟹(x−7)

2

+x

2

=13

2

⟹x

2

+x

2

+49−14x=169

⟹2x

2

−14x+(49−169)=0

⟹2x

2

−14x−120=0

⟹x

2

−7x−

2

120

=0

⟹x

2

−7x−60=0

⟹x

2

−12x+5x−60=0

⟹x(x−12)+5(x−12)=0

⟹(x−12)(x+5)=0

∴x=12 (x=-5 is not possible since side can't be negative)

∴Base=12cm

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