Question

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Answer 1

Answer:

given,

h=32 cm

p=80 cm

B+A+H =80 cm

B+A=80-32

B+A=48 cm

now,

B^2+A^2=H^2

(B+A)^2 - 2 AB=H^2

(48)^2-(32)^2=2×A×B

(48+32)(48-32)=2 AB

80×16/2 =AB

640=AB

THEN,

area of triangle = 1/2×A×B

                          =1/2×640

                          =320 cm

Answer 2

Let one of the side of the triangle be a

Let another side of the triangle be b

a + b + 32 = 80 cm

a + b = 80 - 32

a + b = 48 ---- eq(1)

By phythgoras theorem

a² + b² = 32²

(x + y)² - 2xy = 32 × 32

Since x² + y² = (x + y)² - 2xy

(48)² - 2ab= 1024 (from eq(1))

2304 -2ab = 1024

2ab = 2304 - 1024

2ab = 1280

ab = 1280/2

ab = 640 -----eq(2)

Area of the right angled triangle = 1/2 × Base × Height

In right angled triangle the 2 sides other than hypotenuse are base and height of the triangle. Here base is a and height is b.

= 1/2 × a × b

= 1/2 × ab

= 1/2 × 640 (from eq(2))

= 320cm²

So Area of the right angled triangle = 320 cm²

So answer is (B) = 320 cm²