Question

an architect design the enterway of the restaurant she wants to put the triangular windows above the doorway due on the energy retraction the window can only have an area of 120 square feet and the architect wants to be base to be 44 feet more than twice the height find the base and the height of the window​

Answer 1

Given :- the window can only have an area of 120 square feet and the architect wants the base to be 44 feet more than twice the height .

To Find :-

• find the base and the height of the window ?

Solution :-

Let us assume that, the height of the window is x feet .

then,

• Area of triangular window = (1/2) * Base * height .

So,

→ Base = 2 * x + 44 = 2x + 44 = 2(x + 22)

→ Height = x

then,

→ (1/2) * 2(x + 22) * x = 120

→ x² + 22x - 120 = 0

Now, Sridharacharya formula for Solving Quadratic Equation ax² +bx + c = 0 says that,

• x = [ -b±√(b²-4ac) / 2a ]
• x = [ - b± √D /2a ] where D(Discriminant)= b²- 4ac.

here we have ,

• a = 1
• b = 22
• c = (-120)

So,

→ D = (22)² - 4 * (-120) * 1

→ D = 484 + 480

→ D = 964

then,

→ x = [ - 22 ± √964 ] / 2 * 1

→ x = (-22 ± 31.04)/2

→ x = (-22 + 31.04)/2 = 4.52

or,

→ x = (-22 - 31.04)/2 = (-26.52) .

{ Since height in negative value not possible.}

Therefore,

→ Height of window = 4.52 feet .

→ Base of window = (2 * 4.52 + 44) = 53.04 feet .

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