Question

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Answer 1

Answer:

Let ABC be a right angled triangle with right angle at B

let AB=5x and BC=3x−1.

Then, area =△ABC=

2

1

(Base×Height))

⇒60=

2

1

(AB×BC)⇒60=

2

1

×5x(3x−1)

⇒120=5x(3x−1)⇒3x

2

−x−24=0⇒3x

2

−9x+8x−24=0

⇒(x−3)(3x+8)=0⇒x=3or3x+8=0⇒x=3orx=−

3

8

⇒x=3

AB=5x=5×3=15cm and BC=(3x−1)=(3×3−1)=8cm

Now, AC

2

+AB

2

+BC

2

⇒AC

2

=15

2

+8

2

⇒AC

2

=289⇒AC=17cm

Hence, hypotenuse =17cm

Step-by-step explanation:

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Answer 2

Perimeter=15+8+17=40cm

Semiperimeter = 40/2 = 20cm

3- 3x+3x+2x=32

8x=32 , x = 32/8 = 4cm

SO BASE = 2×4=8CM

HEIGHT=

H²=h²+b²

12²=h²+4²

144=h²+16

h²=144-16

h=11.31

area=1/2×11.31×8=45.24cm

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