Question

The perimeter of a right triangle is 60 cm It's hypotenuse us 25 cm. Find the area of the triangle ? ​

Answer 1

$\bf\underline{\underline{\green{SOLUTION:-}}}$

Question

• The perimeter of a right triangle is 60 cm It's hypotenuse us 25 cm. Find the area of the triangle ?

Answer

• Area = 150cm²

Given

• Perimeter = 60cm
• hypotenuse = 25cm

To Calculate

• Area of triangle __?

Explanation

Let ABC be the Given right angled triangle

Let , Base = Xcm

hypotenuse = 25cm

Perimeter = 60cm

AB+BC+AC = 60

➺ AB +x+25=60

➺ AB =35-x

By Pythagoras theorem

h²= p²+b²

➺ 25²= (35-x)²+x²

➺ 2x²-70x+600=0

➺ x²-35x+300=0

➺ x²-20x-15x+300=0

➺ x(x-20)-15(x-20)=0

➺ (x-20)(x-15)=0

x=20 or x=15

If x= 20 Then,

AB = 35-x = 35-20 = 15

BC = x = 20

${\boxed{\red{\tt{Area = 1/2×b×h}}}}$

➺ 1/2 × 20×15

➺ 1/2 × 300

➺ 150cm²

$\bf\underline{\underline{\green{HENCE:-}}}$

• Area = 150cm²

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