Question

the area of a right triangle is 90 cm². the two sides containing the right angles are 15 cm and 6 cm.​

Answer 1

Step-by-step explanation:

Given: In a right angled triangle, Perpendicular = 5x and Base = 3x - 1

Area = 60 cm

2

Area of triangle =

2

1

(base)(height)

60=

2

1

(5x)(3x−1)

120=15x

2

−5x

24=3x

2

−x

3x

2

−x−24=0

3x

2

−9x+8x−24=0

3x(x−3)+8(x−3)=0

(3x+8)(x−3)=0

x=3,

3

−8

Neglect the nagative value, x=3

Thus, perpendicular = 15 cm and base = 8 cm

Now, from Pythagoras theorem,

H

2

=P

2

+B

2

H

2

=15

2

+8

2

H

2

=225+64

H

2

=289

H=17cm