Question

The perimeter of a right-angled triangle is 60cm.Its hypotenuse is 26cm.The area of the triangle is​

Answer 1

Answer:

★ Area = 120 cm² ★

Step-by-step explanation:

Given:

• Perimeter of right angled triangle is 60cm
• Hypotenuse of the triangle is 26 cm

To Find:

• Area of right angled triangle

Solution: † Perimeter of triangle= a + b + c and we can write area as $\large{\sf {\frac{</strong><strong>ab</strong><strong>}{2}}}$ which is same as $\large{\sf {\frac{<strong>1</strong>}{<strong>2</strong>}}}$ x Base x Height

A/q

→ 60 = a + b + c

→ 60 = a + b + 26

→ 60 – 26 = a + b

→ 34 = a + b..........( 1)

Also, By Pythagoras Theorem

→ a² + b² = c²

→ a² + b² = 26²

→ a² + b² = 676...........(2)

★ Squaring on both sides of equation 1

→ 34² = ( a + b )²

→ 1156 = a² + b² + 2ab

→ 1156 = 676 + 2ab [ From equation 2 ]

→ 1156 – 676 = 2ab

→ 480 = 2ab [ Divide both sides by 4 ]

→ 120 = $\large{\sf {\frac{</strong><strong>ab</strong><strong>}{2}}}$

Hence, The area of the ∆ is 120 cm²