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govardhan

· started a discussion

· 1 Months ago

any shourtcut answer please (Question:1096101.0)

other method

Question:

A right angled triangular plot of area 150 m2 is to be enclosed by a wire of length 60 m. Find the length of the longest side of the plot.

Options:
A)

20m

B)

24m

C)

26m

D)

25m

Solution:

Ans: (d) 

Let the two sides, other than the longest side, of the plot be h and b. Then the longest side hypotenuse a = √(b2 + h2) 

Based on Pythagoras theorem, 

h2 + b2 = a2 ----(1) 

Based on area, 

1/2 b h = 150

b h = 300 ------(2) 

perimeter of triangle = b + h + a = 60 

h + b = 60 - a ----(3) 

By solving equations(1), (2) & (3) 

From (3), 

h + b = 60 - a 

(h + b)2 = (60 - a) 2 

h2 + b2 + 2hb = 60² + a² - 120a ---(4) 

Substitute (1) and (2) in (4): 

h2 + b2 + 2hb = 602 + a2 - 120a 

(h2 + b2) + 2(hb) = 602 + a2 - 120a 

a2 + 2(300) = 3600 + a2 - 120 a 

3000 = 120a 

a = 25m 

The length of the longest side is 25 m.

Knowledge Expert

· commented

· 1 Months ago

Dear student,
We will provide you video solution.

Regards
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