Question

One side of a right triangle measures 20 cm and the difference in length of its hypotenuse and other side is 8 cm.Find the measure of its unknown sides and calculate its area Verify the result using heron's formula.

Answer 1

Step-by-step explanation:

Let h= 126m and base = b m and Hypotenuse = h m

By pythagorous therem, we have h2 = b2 + (126)2

h2 -b2 = (126)2

(h+b)(h-b) = (126)2

It is given that h-b = 42 m

(h+b)*42= 126*126

h+b = 126*126/42

h+b= 3*126 = 378.....(1)

h-b = 42.....(2)

Adding eq(1) and (2), we get

2h= 420

h = 420/2=210m

Now h-b= 42

210-b =42

b= 210-42= 168m

Area = b*h/2

A= 168*126/2

A= 10584 m2

a=126m ,b=168m and c= 210m

s= a+b+c/2 = 126+168+210/2 = 504/2=252m

A = √s(s-a)(s-b)(s-c)

A= √252.(252-126)(252-168)(252-210)

A= √252*126*84*42

A= 10584m2

Answer 2

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