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
so sides are 8,6
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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