Solve.
-A triangle is 8 cm wider than it is tall. The area is 280 cm2. Find the width (length of the base). h + 8
A)20 cm
B)8 cm
C)28 cm
D)29 cm

Question

Quizplus · Accepted Answer

Let's call the height of the triangle "h" and the width or base of the triangle "w".
From the problem, we know that:

w = h + 8

We also know that the area of the triangle is:

(1/2) * base * height = (1/2) * w * h = 280

Substituting the first equation into this one to eliminate "w", we get:

(1/2) * (h + 8) * h = 280

Multiplying both sides by 2 to simplify, we get:

(h + 8) * h = 560

Expanding the left side, we get a quadratic equation:

h^2 + 8h - 560 = 0

We can factor this equation or use the quadratic formula to solve for "h".
Using the quadratic formula, we get:

h = (-b ± sqrt(b^2 - 4ac)) / 2a

Plugging in the values of "a", "b", and "c" from our quadratic equation above, we get:

h = (-8 ± sqrt(8^2 - 4*1*(-560))) / 2*1

Simplifying this, we get:

h = (-8 ± sqrt(3368)) / 2

We can ignore the negative solution since height can't be negative in this context. Calculating the positive solution, we get:

h ≈ 22.51

Finally, we can use either equation w = h + 8 or the area equation (1/2) * w * h = 280 to solve for "w". Using the first equation, we get:

w = h + 8 ≈ 30.51

Rounding this to the nearest whole number, we get w ≈ 30 cm, which is closest to choice C.

Solve. -A Triangle Is 8 Cm Wider Than It Is Tall