Question

The perimeter of a right triangle is 30 cm .its hypotenuse is 13 cm and base is 5 cm .find the area of the triangle

Answer 1

Let the legs of the right triangle be 'a' and 'b'. Let the hypotenuse be 'h'.

Perimeter, p = a + b + h = 30 cm

p = a + b + 13 cm = 30 cm

a + b = 30 - 13 = 17 cm

a = 17 - b …………… (1)

By Pythagoras Theorem

a² + b² = h²

(17 - b)² + b² = 13² ................ From (1)

b² + 17² - 34b + b² = 169

2b² - 34b + 289 - 169 = 0

2b² - 34b + 120 = 0

b² - 17b + 60 = 0

b² - 12b - 5b + 60 = 0

b(b - 12) - 5(b - 12) = 0

(b - 12)(b - 5) = 0

b = {12, 5}

From (1)

a = 17 - 12 = 5 cm, or a = 17 - 5 = 12 cm

a = {5,12}

The right triangles is (5 cm, 12 cm, 13 cm)

Alternatively,

The given details points to a trivial Pythagorean Triple (5,12,13).

Checking, 5+12+13 = 30.

It is a scalene right triangle.

Answer 2

Answer:

Step-by-step explanation:

Hy 13cm

Base 5cm

Perpendicular 30-18=12cm

Area = 1/2*perpendicular* height

1/2*12*5

30Cm²