Given that area of angle of ABC is 24 cm squared, determine the area of angle PQR

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Stuckonhomework

17.04.2023

Mathematics

20 m long,

each piece of cloth for $10

Step-by-step explanation:

Let x m be the length of the piece of cloth.

Original cloth:

Length = x m

Cost = $200

Cost per meter $\dfrac{\$200}{x}$

Changed cloth:

Length = x + 5 m (5 m longer)

Cost = $200

Cost per meter $\dfrac{\$200}{x}-\$2$ (each metre of cloth was $2 less)

Hence,

$\left(\dfrac{200}{x}-2\right)\cdot (x+5)=200$

Multiply the equation by x:

$(200-2x)(x+5)=200x\\ \\200x+1,000-2x^2-10x=200x\\ \\-2x^2-10x+1,000=0\\ \\x^2+5x-500=0\\ \\D=5^2-4\cdot(-500)=25+2,000=2,025\\ \\x_{1,2}=\dfrac{-5\pm\sqrt{2,025}}{2}=\dfrac{-5\pm 45}{2}=-25,\ 20$

The length cannot be negative, so x = 20 m, each metre for $10.

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