Question

the area of a triangular garden is 200 square feet. If the base is 30 feet more than its height, what is the base of the garden?

Answer 1

The base of the triangular garden is calculated as 40 ft

The given parameters include:

• the area of the triangular garden, A₁ = 200 ft²

• let the height of the triangular garden = h

• the base of the triangular garden, b = 30 ft + h

The area of a triangle is given as;

$Area \ = \frac{1}{2} \times \ base \times \ height\\\\A = \frac{1}{2} bh\\\\2A = bh\\\\b = \frac{2A}{h} \\\\Recall, \ b= 30 + h\ \ \ and \ A = 200\\\\30+ h = \frac{2(200)}{h} \\\\30 \ + h = \frac{400}{h} \\\\30h + h^2 = 400\\\\h^2 + 30h - 400= 0\\\\Factorize \ the \ above \ expression\\\\h^2 + 40h- 10h- 400 = 0\\\\h(h + 40) - 10(h + 40) = 0\\\\(h- 10)(h+40)= 0\\\\h = 10 \ \ or \ \ -40\\\\since\ the \ height \ can't \ b e\ negative\\\\h = 10 \ ft$

Now solve for 'b' = 30 ft + 10 ft  =  40 ft

Therefore, the base of the garden is 40 ft

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