Grace and her brother Sid want to raise money to go to band camp. Their parents have agreed to help them earn up to $400 by payi
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Given:
The base of the triangle = 6 ft
The height of the triangle = 5 ft
The other two side of the triangle = 5.5 ft and 5.5 ft
The height of the prism = 9 ft
To find the measurement of the fabric to make the tent.
We need to find the surface area of the triangular prism.
Formula
The surface area of the triangular prism is
where, b be the base of the triangle
h be the height of the triangle
a and c be other two sides of the triangle
H be the height of the prism
Now,
Putting,
b = 6, h = 5, a = 5.5, c = 5.5 and H = 9 we get,
sq ft
or, sq ft
or, sq ft
Hence,
Based on the given dimension 183 sq ft fabric is needed to make the tent.
We know from the problem that l = 3w - 5. We also know the formula for area is A = w * l. Therefore, the area of the rectangle is A = w * (3w - 5). We can then set this equation equal to 50 as the question states and solve for w.
Expand the multiplication
Subtract 50 from both sides.
We now have a quadratic equation and can solve it using the quadratic formula to find w. We find that the solutions to the equation are 5 and -3.3. We know that the width can't be negative, so the width must be 5.
Finally, we can plug this solution into the length formula we found earlier to solve for length.
Plug in the solution to w.
Multiply 3 and 5.
Subtract 5
Therefore the width is 5 and the length is 10.
Expand the multiplication
Subtract 50 from both sides.
We now have a quadratic equation and can solve it using the quadratic formula to find w. We find that the solutions to the equation are 5 and -3.3. We know that the width can't be negative, so the width must be 5.
Finally, we can plug this solution into the length formula we found earlier to solve for length.
Plug in the solution to w.
Multiply 3 and 5.
Subtract 5
Therefore the width is 5 and the length is 10.