Question

7. The perimeter of a right triangle is 60 cm and its hypotenuse is 25 cm. Find the area of the triangle.

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Answer 1

150 cm²

Explanation:

Given

• Perimeter = 60 cm
• Hypotenuse = 25 cm

Solving

• We need to find the lengths of the altitudes
• Since 25 cm is already covered there is (60 - 25) = 35 cm remaining
• The lengths can be taken as x and 35 - x
• Now, since it's a right triangle, we can solve for x using the Pythagorean Theorem

Applying the theorem

• x² + (35 - x)² = 25²
• x² + 1225 - 70x + x² = 625
• 2x² - 70x + 600 = 0
• x² - 35x + 300 = 0
• x = 35 ± √1225 - 4(1)(300) / 2
• x = 35 ± √25 / 2
• x = 35 ± 5 / 2
• x = 40/2 = 20 or x = 30/2 = 15
• Upon solving the lengths of the altitudes are 15 and 20

Area of the triangle

• 1/2 x product of the altitudes
• 1/2 x 15 x 20
• 10 x 15
• 150 cm²