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A triangle is $10 \mathrm{cm}$ wider than it is tall. The area is $48 \mathrm{cm}^{2} .$ Find the height and the base.CAN'T COPY THE IMAGE
$16 \mathrm{cm}$, $6 \mathrm{cm}$
Algebra
Chapter 6
Polynomial Factorizations and Equations
Section 7
Applications of Polynomial Equations
Graphs and Statistics
Exponents and Polynomials
Equations and Inequalities
Polynomials
Missouri State University
Campbell University
Harvey Mudd College
Lectures
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Okay, so the question we're going to be looking at today is were given a triangle, and the triangle is 10 centimeters wider. Then it is tall. Oh, then told, um so in the area 48 si m squared. Um, so the first thing we're gonna do is we're gonna let X equal height, and then we're gonna let X plus 10 equal the base. Uh, because the base is the witness 10 centimeters longer than the height. Uh, the area of the triangle is 1/2 base times height. That's the area of a triangle. So in this case, we're gonna plug in all our numbers, so we know that the area is 48 equals 1/2. Um, the base we figured it out was X plus 10. And then the height is just X. Uh um, So the first thing we're gonna do is we're gonna try Teoh, simplify this equation, multiply both sides by two. So that's gonna cancel. Cancel the side by two. Originally left with 96 equals X plus 10 and X. Ah, we're going to distribute, um, this So we're gonna a we're going to get 96 is equal to X squared plus 10 x Bring the 96 over to set the side equals zero. So it's gonna be zero is equal to X squared plus 10 x minus 96. We're gonna have to factor this to find are two values. You can either do the quadratic equation or go through. If I guess your check. Either way, you're gonna find out you're factors are gonna be 16 and negative six. So we're gonna be left. Zero is equal to X plus 16 x minus six. So that leaves us with X equals negative 16 and X equals six. Um, so because, um, because they were dealing with area, this number cannot be negative. So X has to be 16. We know from the question that the that the with has to be 10 centimeters longer than the height or wider than the height. And we see that, um, 16 is 10 centimeters longer. Their 10 game. It's bigger than six. So obviously 16 is the no no race that is the base, Um, and six is be height. Obviously, you're gonna want to read it there for a statement using the proper unit. So the beef is 16 centimeters and hate is six centimeters. And that's your answer.
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