The perimeter of a right triangle is 60 cm. Its hypotenuse is 25 cm. Find the area of the triangle.
Answers
Step-by-step explanation:
Given :
Perimeter of a right angled triangle is 60cm.
Its hypotenuse is 25cm.
To find :
Area of the triangle.
Solution :
Let ABC be the right angled triangle, where BC = x cm.
Perimeter of triangle = Sum of all the sides of a triangle
- AB + BC + CA = 60 cm
- AB + x + CA = 60 cm
- AB + x = 60 - 25
- AB + x = 35
- AB = 35 - x
Using Pythagoras theorem,
- AB² + BC² = AC²
⇒ (35 - x)² + (x)² = 25²
⇒ 2x² - 70x + 625 = 0
⇒ 2x² - 40x - 30x + 625 = 0
⇒ 2x(x - 20) -30(x - 20) = 0
⇒ (x - 20)(2x - 30)=0
∴ x = 20 or 15
If x = 20 cm,
- AB = 35 - 20
- AB = 15 cm
Area of triangle,
⇒ 1/2 × base × height
- 1/2 × BC × AB
- 1/2 × 20 × 15
- 150 cm²
If x = 15 cm,
- AB = 35 - 15
- AB = 20 cm
Area of triangle,
⇒ 1/2 × base × height
- 1/2 × BC × AB
- 1/2 × 15 × 20
- 150 cm²
∴ Area of the triangle is 150 cm².
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Answer:
Let ABC be the given right angled triangle such that base=BC=x cm and hypotenuse AC=25cm
Now, perimeter =60cm
AB+BC+AC=60
AB+x+25=60
AB=35−x
By Pythagoras theorem, we have
AB
2
+BC
2
=AC
2
⇒(35−x)
2
+x
2
=25
2
⇒2x
2
−70x+600=0
⇒x
2
−35x+300=0⇒x
2
−20x−15x+300=0⇒(x−20)(x−15)=0⇒x=20orx=15
If x=20, then AB=35−x=15 and BC=x=20
Area =
2
1
(BC×AB)=
2
1
(20×15)=150cm
2
If x=15, then AB=35−x=20 and BC=x=15
Area =
2
1
(BC×AB)=
2
1
(15×20)=150cm
2
Step-by-step explanation: