Step-by-step explanation:
h = height of rectangle (should be "length", but ok)
w = width of rectangle
w = h + 97
the diagonal of the rectangle is the Hypotenuse (baseline) of a right-angled triangle with the legs being one height and one width side of the rectangle.
so, we use Pythagoras
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle).
diagonal² = h² + (h + 97)² = h² + h² + 2×97h + 97²
113² = 12769 = 2h² + 194h + 9409
3360 = 2h² + 194h
1680 = h² + 97h = (h + 97/2)² - 9409/4
(completing the square)
6720/4 + 9409/4 = (h + 97/2)²
16129/4 = (h + 97/2)²
127/2 = h + 97/2
30/2 = h = 15
the height is 15.0 in
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Answer:
15+sqrt(235), 15-sqrt(235)
Step-by-step explanation:
X^2-30x-10=0
Use quadratic formula (b+-sqrt(b^2-4(a)(c)))/(2(a))
a=1, b=-30, c=-10
Answer: 24 miles
Step-by-step explanation: 12 mph is two times as fast as 6 mph so 6 hours round trip is 2 hours for bike and 4 hours for jogging. You can either plug 2 for 12 (bike) or 4 for 6 (jog) either way you get 24
Answer: 14.86 yards
Step-by-step explanation:
A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height and the longer base to be 7 yards greater than the height. She wants the area to be 295 square yards. The situation is modeled by the equation …