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

KnowledgeBoat · Accepted Answer

Let △ABC be the right triangle. We know that, Perimeter of a right-angled triangle = 60 cm Hypotenuse = 25 cm So, the sum of other two sides of triangle = 60 – 25 = 35 cm Let, base (BC) = x cm So, AB = (35 - x) cm Using the Pythagoras theorem, ⇒ AC2 = AB2 + BC2 ⇒ 252 = (35 - x)2 + x2 ⇒ 625 = 1225 + x2 - 70x + x2 ⇒ 2x2 - 70x + 600 = 0 Dividing by 2 on both sides, ⇒ x2 - 35x + 300 = 0 ⇒ x2 - 15x - 20x + 300 = 0 ⇒ x(x – 15) - 20(x - 15) = 0 ⇒ (x - 15)(x - 20) = 0 ⇒ x - 15 = 0 or x - 20 = 0 ⇒ x = 15 or x = 20. If x = 15, then 35 - x = 35 - 15 = 20 cm. If x = 20, then 35 - x = 35 - 20 = 15 cm. So, length of other two sides apart from hypotenuse are 15 cm and 20 cm. Area of triangle = × base × height Substituting the values we get, A = × 15 × 20 = 150 cm2. Hence, area of triangle = 150 cm2.

Mathematics

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

Mensuration

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