Math, asked by Thirupathi5831, 1 year ago

The perimeter of a right angled triangle is 24cm.If its hypotenuse is 10cm find the other two sides. Find its area using the formula area of a triangle.

Answers

Answered by ayyappasunandapd8d4q
14
simply we say that 10^2= 8^2+6^2
so sides are 8,6
Attachments:
Answered by himanshu4967
7

Answer:

24cm²

Step-by-step explanation:

Let the two sides be 'a' and 'b'

Perimeter = Sum of all sides

24cm = a+b+10cm

24cm-10cm = a+b

a+b = 14 cm ----------------i

In the triangle by pythagoras theorem

a²+b² = hypotenuse²

a²+b² = (10 cm)²

a²+b² = 100 cm² ----------------ii

From i

a+b = 14 cm

(a+b)² = (14 cm)²

a²+2ab+b² = 196 cm²

100 cm²+2ab = 196 cm² ------------- from ii

2ab = 196 cm² - 100 cm²

ab = 96 cm²

ab = 96cm²

2

ab = 48 cm²

(a-b)² = (a+b)²- 4ab

= a²+2ab+b²-4ab

= a²-2ab+b²

= 100 cm²- 2×48 cm²

= 100 cm²-96cm²

= 4 cm²

(a-b) = 4 cm²

a-b = 2-----------iii

From adding i and ii

a + b = 14 cm

a - b = 2 cm

(+) (-) (+)

2a = 16 cm

a = 16cm

2

a = 8cm

a+b = 14cm--------- From i

8cm+b = 14cm

b = 14cm-8cm

b = 6cm

Area of triangle = 1 ×b×h

2

= 1 ×8cm×6cm

2

= 24 cm²

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